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Rm 330: I don't need to… Who bearing.

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Rm 330: He is one of the most influential condensed meta-theorists working today.

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Rm 330: Let me just mention that, Subir is a member of the National Academy of Sciences, and of, foreign member of Royal Academy of Sciences, you know, Onsiger, Price.

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Rm 330: And, why is the rock medalist, actually?

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Rm 330: So, and please also come to the colloquium tomorrow. So today, Subir will, for a seminar, he'll talk about, you know, SU2 gauge theory for intertwined orders and whole pockets in the corporate sugar case.

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Rm 330: Thank you very much, Anil. It's,

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Rm 330: I have a pleasure to be back here in Rutgers, or visit

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Rm 330: Many times, and have many good friends.

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Rm 330: So, please be quite informal, please feel free to interrupt anytime.

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Rm 330: So, there was a time I didn't have to introduce the cube rights, but those times are gone now, I have to remind, especially the younger people.

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Rm 330: Why we're still interested in the cube rates.

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Rm 330: So, the reason for my talk, partly, is I think there's been a lot of theoretical progress in the last 10 years, which are really…

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Rm 330: Bringing us closer to answering the very difficult questions.

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Rm 330: And secondly, I'll show you some very recent experiments from last year.

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Rm 330: Which are giving you information. So…

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Rm 330: The field has continued to develop over 30 years.

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Rm 330: And one thing I'll say in defense of the cuprates, is still the very best superconductor out there, except those under extremely high pressure.

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Rm 330: But if you want something you can hold in your hand and make devices out of.

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Rm 330: This is still the best game in town.

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Rm 330: So it's worth to understand it.

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Rm 330: Alright, so these are materials.

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Rm 330: And in fact, the difference between the different materials will be important for some of my discussion.

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Rm 330: Predominantly, they have a square lattice of copper atoms.

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Rm 330: And mostly, that's all I'll talk about.

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Rm 330: But for one of the experiments, we also have to think about the structure in the third direction, and I'll come to that.

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Rm 330: When I get there.

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Rm 330: Okay, so… For now, we just think of it as square lattice with one orbital per site.

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Rm 330: When P is 0, is exactly one electron.

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Rm 330: On each orbital, and they form an anti-ferromagnet with this tigered arrangement of space.

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Rm 330: Then you could dope it at density P, and that's when you get the high DC superconductor.

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Rm 330: And here, P is the number of holes relative to the antithromagnetic, so that the density of holes is P in this picture.

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Rm 330: However, if I was a band theorist or a semiconductor person, Or density functional theory.

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Rm 330: then that's not how to count the electrons, or even the holes.

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Rm 330: The number of electrons, as you can just see, is 1 minus P.

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Rm 330: And the number of holes, in band theory, is 1 plus P, it's not P.

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Rm 330: That's because when you count holes in a semiconductor, you count holes

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Rm 330: With respect to a film there.

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Rm 330: And in the film band, there's 2 electrons per second.

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Rm 330: So… As far as solid-state physics is concerned, from pre-1980,

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Rm 330: The number of holes here is 1 plus P.

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Rm 330: The number of electrons, 1 minus B.

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Rm 330: So the way you measure the density of carriers.

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Rm 330: is by doing the Hall effect of photomation.

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Rm 330: And in this case, if you… at these large values of P, you indeed see a Hall coefficient.

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Rm 330: of holes of density 1 plus B.

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Rm 330: Now, why is it holes and not electrons?

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Rm 330: that, as photomissions sold into the shape of the Fermi surface.

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Rm 330: If you look at the holes, they formed a nice circular foaming surface.

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Rm 330: Should look at the electron, it's open.

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Rm 330: So it's much better to think in terms of holes rather than electrons.

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Rm 330: That has nothing to do with…

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Rm 330: Any interaction? It's just a question of the band structure.

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Rm 330: Okay, so that's the part that's reasonably well understood.

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Rm 330: But that's why TC is very low.

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Rm 330: If you go to the other end.

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Rm 330: then that's where all the mysteries start, which I'm going to talk about today.

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Rm 330: So here, again, look at the whole coefficient.

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Rm 330: There's definitely a regime, but it's temperature independent.

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Rm 330: and gives you density P, which is what you very naively might have thought, Starting from the anti-format.

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Rm 330: But the only trouble is, There is no anti-ferromagnet. Anti-ferromagnetism disappears.

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Rm 330: appear on 0.04 or 0.05.

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Rm 330: And this behavior is seen.

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Rm 330: To much larger values of peace.

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Rm 330: So that's the essential mystery.

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Rm 330: At least what's called the surrogap regime.

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Rm 330: Where, how do you get… balls of her periago density P,

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Rm 330: In a regime where there's no obvious antiferromagnet.

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Rm 330: Oh.

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Rm 330: And furthermore, when we look at the photomission.

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Rm 330: You see these strange Fermi arcs.

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Rm 330: Where…

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Rm 330: you know, the Fermi surface have been truncated, if you wish. These are the so-called antenodal regions, where there's a gap.

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Rm 330: And there seems to be some kind of arc.

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Rm 330: All right, well, there's nobody's theory that a zero temperature has an arc.

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Rm 330: But this might… maybe this is a finite temperature effect.

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Rm 330: But as I'll discuss, there are theories where Okay.

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Rm 330: At zero temperature, you get a pocket.

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Rm 330: And in fact, this was a hypothesized in this paper with Peter Johnson. It's a photo emission paper.

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Rm 330: And through some somewhat questionable extrapolation technique, they seem to have hypothesized, well, the arcs actually

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Rm 330: Closed into a pocket.

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Rm 330: Anyway, okay, so that's the debate that's been going on for now over… over 15 years.

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Rm 330: And I'll give you my opinion.

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Rm 330: On what the answer is. Soon.

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Rm 330: There's also these STM measurements.

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Rm 330: Where they do quality boretical interference for different values of P, and what they… they show something roughly consistent with forward emission, what I just showed you. At small P, you just see the arcs.

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Rm 330: And then suddenly, at some… particle P, where the pseudo gap disappears.

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Rm 330: That's where… that's the most interesting regime, really, where that's why they have the highest DC.

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Rm 330: You get the big… conventional Fermi surface.

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Rm 330: That you would get.

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Rm 330: No bad theory.

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Rm 330: Okay.

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Rm 330: So, there are many, of course, many, many papers on this mysterious pseudo-gap regions.

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Rm 330: And almost all of them, at least one… well, there are two broad families, the big broad…

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Rm 330: One broad family is, well, this is some kind of

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Rm 330: Fluctuating regime, where there's some broken symmetry.

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Rm 330: There's D wave superconductivity, there's charge density wave, there's antifromagnetism.

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Rm 330: And somehow they're intertwined and suddenly perpetuating.

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Rm 330: And that's how you understand it, so just one big thermal mess.

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Rm 330: Although, in this theory, it's rather hard to even understand why you should get a Hall coefficient of density P, which is temperature independent. Can you comment on the T-star scale?

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Rm 330: I won't, but that's when the pseudogap disappears in a strange metal.

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Rm 330: So strange, what we have, huh? Just, like, from, observations when they've been…

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Rm 330: Oh, I don't know, it maybe has to do kinks in the resistivity, there's kinks in other thermodynamic properties.

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Rm 330: And they all roughly consistent.

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Rm 330: I think these authors debate around a couple years before settling on this as a consensus line.

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Rm 330: Yeah, it's not connected to the Hall change. No, that's quite temperature-dependent. You're not talking about the low temperature hull effect.

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Rm 330: Oh.

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Rm 330: This… in a sense, this strange matter is the topic for yet tomorrow's forecast, so we can return to that point.

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Rm 330: Today, I want to stick to the yellow region and lower temperature.

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Rm 330: Alright.

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Rm 330: So…

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Rm 330: The central argument would be that, in fact, I don't think that's the right way to think about it. It's not a thermally fluctuating, some conventional ordered state. It's really representing a new type of quantum ground state with spin-liquid type correlations.

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Rm 330: It's the state that we call ethyl star, and I'll describe What it is very shortly.

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Rm 330: So…

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Rm 330: We go at it in sort of the opposite point of view. We say that, first of all, there is a quantum state.

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Rm 330: which we call the FL star.

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Rm 330: And just like the Fermi liquid is ultimately unstable to superconductivity, you have charged density waves.

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Rm 330: Similarly to this exotic state is also unstable, so if, kind of.

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Rm 330: Changing, you know, putting… taking the position of the cart and the horse is back to the conventional point of viewing.

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Rm 330: So this explains the whole effect. No trouble.

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Rm 330: And then… I'll talk about the very recent experiments.

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Rm 330: Which show that whatever's causing the Hall effect

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Rm 330: It's also able to tunnel coherently between layers.

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Rm 330: And that also puts very strong constraints on the morals.

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Rm 330: And it's hard to see how the point 2 can come from the other models.

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Rm 330: Okay, and then once you have this, description of Echo star, then…

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Rm 330: You can think about these instabilities, And I'm liking…

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Rm 330: Thermi liquid is where you do RPA, VCS theory.

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Rm 330: Here, you really have to do… deal with the gauge theory.

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Rm 330: And use a Higgs field, which behaves like a fractionalized order.

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Rm 330: So this will be the… one of the main things I will explain very shortly.

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Rm 330: All right, so first let me explain what is this proposed

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Rm 330: Quantum state, which is behind the phenomenology of the anecute race.

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Rm 330: Except to click.

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Rm 330: So, the fundamental result… in… solid-state physics is that

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Rm 330: An electron gas, no matter how strong they interacted.

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Rm 330: Has a foamy surface.

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Rm 330: And the area imposed by the Fermi surface, is the same as those of free fermions.

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Rm 330: So just ignore all interactions, take pre-ferromiums with the same symmetry as your final state.

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Rm 330: If there's a broken symmetry, break it for free fermions, and then compute the area close by the Fermi surface, and it has to be the same.

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Rm 330: Modulo of true, of course, because, fill bags can always appear in free fermions.

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Rm 330: So I'll measure areas in units of the Brill1 zone, so…

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Rm 330: when I call this area 1,

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Rm 330: Then this area is the density over 2,

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Rm 330: Because the Title II was spin. It's two states at each point.

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Rm 330: So, area, according to larger j, is rho over 2.

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Rm 330: Okay, so the standard proof of this is implicitly perturbative.

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Rm 330: But a very beautiful non-perturbative proof was given by Oji Kawa.

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Rm 330: very… Thought about the fate of the system on a torus and inserted flux.

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Rm 330: And saw how much momentum the system picked up under the influence of the flux.

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Rm 330: So this, in even more modern language, we call an anomaly.

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Rm 330: So there's a certain anomaly the system has, which is anomaly associated with the conservation of charge and translational symmetry.

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Rm 330: And… You know, it's very much like the Lieb-Schols-Madis argument for antiferromagnets.

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Rm 330: This works in 3D as well as 2D? Yes, yes. And so you don't need any adiabatic path or anything, it's just… No, no.

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Rm 330: So this is a… so it is a non-perturbative argument, and it should work for any system.

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Rm 330: Not just to Firm Electric.

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Rm 330: Right.

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Rm 330: Although in this paper, Hashikawa didn't discuss the broad applications, which will be the next slide.

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Rm 330: All right, so this mixture not only between global UN and translation, tells you the same thing as learning.

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Rm 330: But in a much more powerful way.

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Rm 330: Alright.

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Rm 330: So, what…

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Rm 330: Oshikawa's paper told us, which is a paper we wrote a few years later, is that this means there can be other types of metals, which do not obey the Luckinger area.

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Rm 330: So, Oshikawa's are normally… has to be satisfied.

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Rm 330: But you can satisfy common anomalies in different ways.

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Rm 330: And so there is what we call the Ethel Star.

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Rm 330: Where instead of the Fermi surfaces, occupying total area row, Factor 2 for spin.

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Rm 330: They have an area of rho minus what?

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Rm 330: So, exactly what you're seeing in the Hall effect.

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Rm 330: Come on, you lose one, and exactly what.

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Rm 330: And the reason you're allowed to do that

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Rm 330: And the only way you can do that is if you have some other degrees of freedom.

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Rm 330: That emerge in the system, which have their own anomaly.

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Rm 330: And in particular, what we've understood over the last 30 years of

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Rm 330: work on spin liquids in two and higher dimensions. This is really, again, a version of the Liepchild's Matters anomaly. And spin liquids also have anomalies.

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Rm 330: And in fact, for almost all syndicate anybody's ever considered, that anomaly is 1. It's quantized to be 1.

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Rm 330: So, you can shift The area of the Fermi surface, by exactly what?

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Rm 330: In fact, in some very exotic state by some rational number. So there's a quantization here, also. You can't just plot a integer by any amount you want.

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Rm 330: You can validate it by 1.

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Rm 330: In the almost, say, the most common case.

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Rm 330: So if you have 4 pockets, then the area per pocket would be P over 8.

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Rm 330: 4 pockets, and factor of 2 for spin gives you area P over 8.

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Rm 330: So that's the general result.

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Rm 330: And let me know, actually.

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Rm 330: Take a very pedestrian point of view and show you an at least this toy wave function that does this.

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Rm 330: And why this is a little more surprising than you might think. Yes? Any restrictions need to be placed on that spin liquid, so it's supposed to be gapless, I guess, and… No, it could be any.

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Rm 330: It has to have the right hand over it.

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Rm 330: And basically, what that means in the part-on language, is that the number of part-ons per site… number of spin-ons per site is 1. That's a constraint we always put.

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Rm 330: So even when you drop it, the constraint is the anomaly is fixed.

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Rm 330: It doesn't change. What makes it so fixed?

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Rm 330: microscope. That's the nature of the spin liquid. You can only get these

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Rm 330: You could say the anomaly is what makes it fixed. Anomaly is a very general argument, but can't, you know…

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Rm 330: We cannot do the anomal. Yeah.

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Rm 330: Like, I mean, if you take the Tory code, there's many things that are fixed. There's the fractional statistics between… it's always minus 1, no matter what. Anything which is a Z2 fractionization, that's fixed, can't change. That's also connected to another one.

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Rm 330: But you go into it by doping with holes.

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Rm 330: change the anomal thing. That doesn't change the anomaly. I'm sure you are.

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Rm 330: Sorry? Is it engaged anomaly?

197
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Rm 330: It's… no, it's a global symmetry, it's an exclusive anomaly. It's a mixed anomaly between global… between U1 global symmetry, in this case, V-spin rotation.

198
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Rm 330: And translation.

199
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Rm 330: So you need, at least SZ conservation, the way you… So the transistorizing chain doesn't have any such anomaly, but the Beytheans at 3.5 absolutely does. That's the least Schulz-Mein argument. It's the same argument.

200
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Rm 330: Made it a little more rigorous.

201
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Rm 330: by our devices.

202
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Rm 330: Alright, so let's… let me show you how this works. It's really very simple.

203
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Rm 330: Just with a few pictures, you can see it. So we start with an antifromagnet.

204
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Rm 330: And let's form a resonating variance bond spin-up liquid state that Anderson postulated.

205
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Rm 330: You have this coherent superposition of infinite… very large number of dimer configurations, giving a trial wave function.

206
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Rm 330: Alright, so now we're going to dope it.

207
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Rm 330: By removing an electron. So I remove…

208
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Rm 330: Electrons on, say, this side and this side, so on, and that always leaves an unpaired partner there.

209
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Rm 330: Okay.

210
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Rm 330: So, there's a spin-a-half object here, which we call a spin-on, and the spin-on can move around, so they pop there, and move further on. And then there's also this spin zero charge E object.

211
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Rm 330: Which you pull the hole on, and that can also move around.

212
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Rm 330: Alright.

213
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Rm 330: So… So this could be a possible state with hormones moving around.

214
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Rm 330: Now, the hold-ons… And how to do something. There's a finite density of them.

215
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Rm 330: So, the fermion, they have to form a Fermi surface.

216
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Rm 330: And in fact, the density of hologes is exactly P,

217
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Rm 330: So the permit surface size would be P, and the spin liquid of the rest of the electrons are in there.

218
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Rm 330: Oh.

219
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Rm 330: in the resonating valence model. So that's a simple picture of how you violate the Geffener rule.

220
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Rm 330: Well, this turns out not to be the right answer.

221
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Rm 330: Because these hold-ons that are really tied to this entanglement, they can't jump from one way to the other on their own. They can… okay.

222
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Rm 330: So what… what happens? So what is our claim? So our claim is that, in fact.

223
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Rm 330: You have these old ones in Spain, and they're there.

224
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Rm 330: But in the ground state, These holes and spinons can gain energy by just being next to each other.

225
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Rm 330: And this hopping gives you an energy gain, T.

226
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Rm 330: Where the energy cost to create a spin-on of the outerly state is J. Since T is bigger than j.

227
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Rm 330: I claim this always happens, and you form a bound state.

228
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Rm 330: So now this is the state that we call as a star.

229
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Rm 330: You have these dimers, Well, these holes spin-off states.

230
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Rm 330: just moving around, and they're fermions, and they can't be spin-off, and they charge E,

231
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Rm 330: So, as they have the same quantum numbers of the electron, they can tunnel from one layer to the next.

232
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Rm 330: Alright, so… That's all there is to it.

233
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Rm 330: And so now these ones form a Fermi surface.

234
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Rm 330: Because they're fermions. It has to be… they have to satisfy the right anomaly, and they will form a Fermi surface of total density row, because that's the density of the green objects.

235
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Rm 330: So, to summarize, really, what is the nature of the Fermi surface?

236
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Rm 330: But for this kind of state, if you were…

237
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Rm 330: counting all the electrons, like I said before, there's still 1 minus P electrons here, or 1 plus p holes with respect to the fill value, you'll get the area 1 plus P over 2.

238
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Rm 330: But in this entangled spin-liquid state.

239
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Rm 330: As pictured, you only count the green objects.

240
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Rm 330: And so they will give you, from a surface of them, themselves, the area.

241
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Rm 330: per pocket, P over 8.

242
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Rm 330: All of this doesn't really depend upon charge, is that right? I mean, it would be applied to neutral objects.

243
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Rm 330: Well, as long as there's some number conservation. It requires a global G1 symmetry. It doesn't require long-range cooler. No, I know, but it…

244
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Rm 330: I don't need to think of U1 as coming from Charge.

245
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Rm 330: Oh, well, I mean…

246
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Rm 330: Oh, ultimately it does. I mean, because Helium-3 would work, but you do need, you need, you need…

247
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Rm 330: you need both spin and… I mean, the numbers are all done for both spin and charts, but yeah, if you had a spinless system, it could also do this. But forming an entangled state and spinless system that off-filling is a little more tricky, but I guess it's possible.

248
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Rm 330: Okay.

249
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Rm 330: So that's…

250
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Rm 330: There's the area P over 8, and this is really the, I'm saying, the main point of the first part of my talk.

251
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Rm 330: You know, it sounds trivial, but I hope, in the way I presented it.

252
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Rm 330: But in fact, it's not.

253
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Rm 330: So another point of view, which many people have taken.

254
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Rm 330: Is, okay, yeah, you've got some charge moving around. Locally, there's an antifer magnitude.

255
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Rm 330: So let me just imagine that locally there's anti-ferromagnetic order, and compute the dispersion of the holes, and the definite density of them, and then rotationally average the whole thing.

256
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Rm 330: That gives you a very different answer.

257
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Rm 330: So that's what you would do if you were above an antithromagnet.

258
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Rm 330: Which might be appropriate for the electron rope equation, that is a thermally fluctuating.

259
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Rm 330: And there's a factor of two difference.

260
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Rm 330: In the size of the pocket.

261
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Rm 330: So, an ordered antiferal magnet, Your brew on Zone is halved.

262
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Rm 330: So when you're counting permit surface area, you only count the area inside The bubble brutal ends off.

263
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Rm 330: Or another way to say it, you only have two parts.

264
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Rm 330: In this exony spin liquid state.

265
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Rm 330: There is no broken cemetery, so they have really four walk-ins.

266
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Rm 330: So the area here would be BO4, Again, it's B over 8.

267
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Rm 330: And, you know, the POO4 has been measured in numerous folio vision experiments.

268
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Rm 330: And the P over 8 is what I'll now talk about.

269
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Rm 330: Okay, so this factor of 2 tells you that

270
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Rm 330: You know, quantum fluctuations are really very different from thermal fluctuations.

271
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Rm 330: And then the state counting argument, which… the naive argument of just taking a pronoun-disordered antifer omega would be the wrong answer.

272
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Rm 330: All right, one more question. So, can you get this state in a single layer system? Do you need the interlayered transport to stabilize it? Oh, we've… in principle, yes, although there's no proof of it. I've shown you the kind of wave function anyway. Oh, yeah. Is there a Hamiltonian for which this is the ground state?

273
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Rm 330: I don't have one. I mean…

274
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Rm 330: Maybe Pierce has some ideas on that.

275
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Rm 330: Yeah, you could start with, say, some liquid, like the…

276
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Rm 330: But that has… all of the solvable spin liquids have, two sides being in a cell, and the content becomes complicated.

277
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Rm 330: There is no real robust soluble spin liquid with one side clean itself.

278
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Rm 330: That's the hardest case.

279
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Rm 330: You can certainly get the analogous state on condo lattice, and you can pretty much prove on condo lattice that the two-band model does have that.

280
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Rm 330: It's a much harder problem.

281
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Rm 330: Yeah.

282
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Rm 330: Okay.

283
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Rm 330: Even numerically, there's really no evidence, because numerically, people are not looking at a very low temperature where it's a superconductor or charge density, where the argument was

284
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Rm 330: So anyway, but experiments are ahead of events, as I'm not sure if you… Okay.

285
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Rm 330: So, the experiment I'm excited about is called the Yamaji Effect.

286
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Rm 330: And there's a related measurement by Bradshaw.

287
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Rm 330: In a different material, which is a bit more complicated to interpret.

288
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Rm 330: I'll just talk about these.

289
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Rm 330: They're just geology measurements.

290
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Rm 330: In this paper by Chan et al, just published a few months ago in Nature Physics.

291
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Rm 330: So they're looking at this particular material, The mercury-based compound.

292
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Rm 330: Which is not important, that much attention.

293
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Rm 330: But what's beautiful about this particular material

294
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Rm 330: Is that it's a single layer of these square lattices.

295
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Rm 330: With AA stacking. Here's copper, and here's copper. Like, simple AA stacking.

296
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Rm 330: There's none of the other puppets have this simple behavior.

297
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Rm 330: So, when you go to very low temperatures and very high fields.

298
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Rm 330: This system does show quantum oscillations.

299
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Rm 330: That would be down here.

300
00:24:53.490 --> 00:24:55.859
Rm 330: But then there's a charge density wave, and…

301
00:24:56.330 --> 00:24:59.129
Rm 330: It's very similar to YBCO for the experts.

302
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Rm 330: So, what many people have been searching for is something at higher temperatures, surrogate.

303
00:25:05.390 --> 00:25:08.009
Rm 330: What do you see from NATO transport?

304
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Rm 330: So, this is what they see. They measure… they apply, Oh.

305
00:25:15.360 --> 00:25:21.070
Rm 330: magnetic… they've measured the C-axis resistivity, measured the transport in this direction.

306
00:25:21.800 --> 00:25:23.630
Rm 330: Or a field of light is…

307
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Rm 330: At a strange angle, theta and phi.

308
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Rm 330: And all different angles. They scan the resistance in this direction.

309
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Rm 330: feels around 70, 80 Tesla.

310
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Rm 330: I don't want ATCO.

311
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Rm 330: experiment I've done in Los Alamos.

312
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Rm 330: Okay, so if you… so…

313
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Rm 330: The way they interpret the result, they said, well, let's assume their focus. You can… you can make other assumptions. This is the assumption that works immediately.

314
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Rm 330: Of arbitrary size.

315
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Rm 330: Area we don't know.

316
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Rm 330: And just assume a simple cosine dispersion in this direction.

317
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Rm 330: So if I take one of these pockets, this is what the three-dimensional Fermi surface looks like. It's just a slightly warped cylinder. This picture is greatly exaggerated. The wall ring is tiny.

318
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Rm 330: Okay, so now, for such situations, of course, two-dimensional materials.

319
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Rm 330: there was something called the Yamaji effect. I'd never heard of it until I saw this treasure, but people in the field know it well. It's been measured in various organic materials.

320
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Rm 330: And the emoji effect is, the following.

321
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Rm 330: There's a special angle called the emoji angle, in which… There's a peak into resistance.

322
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Rm 330: And what happens at that special angle is that the area of this orbit

323
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Rm 330: orthogonal to the field, is independent of KZ.

324
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Rm 330: It's the same everywhere, to first order in T perk. Of course, it's not exactly the same, but the linear term vanishes at a specimen.

325
00:27:02.150 --> 00:27:07.050
Rm 330: So when the area is the same, it's effectively a flat baron in the KZ direction.

326
00:27:07.260 --> 00:27:09.150
Rm 330: And so the resistance goes up.

327
00:27:10.900 --> 00:27:18.410
Rm 330: Anyway, you don't have to… it's not a quantum interference effect. It doesn't require multiple orbits around the…

328
00:27:20.170 --> 00:27:27.080
Rm 330: Around the Fermi surface, as quantum oscillation is required, it's a weaker, it's a four-bands quantum oscillation.

329
00:27:27.650 --> 00:27:29.070
Rm 330: So, alright.

330
00:27:30.950 --> 00:27:33.899
Rm 330: So here's their data.

331
00:27:35.340 --> 00:27:40.239
Rm 330: As a function of different angles for different values of phi, theta, and phi, the two angles.

332
00:27:40.390 --> 00:27:42.869
Rm 330: And they very nicely see this Yamaji peak.

333
00:27:43.500 --> 00:27:47.399
Rm 330: And this is their theory. We've done, since the beta theory.

334
00:27:47.530 --> 00:27:52.400
Rm 330: With more careful account of the microscopics and get similar results.

335
00:27:52.730 --> 00:27:57.789
Rm 330: And you can see it works very well for the whole range of theta and phi.

336
00:27:58.910 --> 00:28:03.810
Rm 330: And so this success… Convinces them of the correctness of their model.

337
00:28:04.290 --> 00:28:08.159
Rm 330: And then they also,

338
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Rm 330: Estimate the size of the pocket, came up with the number 1.3%.

339
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Rm 330: All right, so I saw that in the paper, I looked up the doping 0.1, and I divided by 8, and I said, that's what we predicted, you know, 15 years ago.

340
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Rm 330: So, obviously, I'm very happy.

341
00:28:25.880 --> 00:28:31.380
Rm 330: Whereas the antifromagnet would give you twice that, much farther away.

342
00:28:32.260 --> 00:28:33.600
Rm 330: Anyway.

343
00:28:33.710 --> 00:28:38.229
Rm 330: So anyway, this is… you may not like all the fittings, but I think…

344
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Rm 330: This is really very strong evidence.

345
00:28:42.350 --> 00:28:47.060
Rm 330: First of all, fermione Terriers that can tunnel between players.

346
00:28:48.030 --> 00:28:51.239
Rm 330: None of the other models really have that busy feature.

347
00:28:51.820 --> 00:29:00.859
Rm 330: Even if you had anti-ferromagnetism, Suppose this was an antithromagnet, and the factor of 2 is an accident.

348
00:29:01.240 --> 00:29:05.050
Rm 330: then you would need the antipheral magnitude to be coherent between layers.

349
00:29:05.600 --> 00:29:11.499
Rm 330: It… you know, you… Swing coverage between the layers for the quasi particle to be able to go

350
00:29:11.700 --> 00:29:13.519
Rm 330: From one layer to the next.

351
00:29:13.700 --> 00:29:16.480
Rm 330: And it definitely isn't. There's essentially no…

352
00:29:16.600 --> 00:29:20.020
Rm 330: No correlation in magnetism between the layers in this form.

353
00:29:20.360 --> 00:29:35.620
Rm 330: Yeah. This is all done under very high magnetic fields. Sure. So what happens to the ground state? This is inside the… So the ground state, we know. If you could lower the temperature, that's been done earlier. No, over here, this building, it's a charge density wave, and how it feels.

354
00:29:36.030 --> 00:29:45.019
Rm 330: And that's it, they see beautiful quantum oscillation, but the trouble with the charge density wave, it reconstructs the Fermi survey, becomes very much harder to interpret.

355
00:29:45.210 --> 00:29:48.720
Rm 330: There are also questions there, which we have addressed, but I won't talk about.

356
00:29:48.840 --> 00:29:53.589
Rm 330: But for photo emission, do they see… Nobody can do photo emission in any testing.

357
00:29:53.990 --> 00:30:07.690
Rm 330: That would be the experiment to do, but that's impossible. What's the relation of the angle and the doping? What's the formula? I don't have it here, I'm sorry. It's some trigometric formula.

358
00:30:07.850 --> 00:30:13.149
Rm 330: Okay, MRG, and… And… and if. PF.

359
00:30:13.800 --> 00:30:18.999
Rm 330: Yeah, so all you need to know, sorry, the only thing you need to know to get the emanji angle

360
00:30:19.140 --> 00:30:22.600
Rm 330: Is… is the C-axis spacing.

361
00:30:22.720 --> 00:30:24.679
Rm 330: You know the CX is spacing?

362
00:30:24.950 --> 00:30:34.850
Rm 330: and you know the Yumagi angle, you can read off the size of the Ferming surface. Respectively, of the details of the mass structure? It has to be cosine in this direction.

363
00:30:34.940 --> 00:30:48.110
Rm 330: Oh, I see. Well, and you assume you can… elliptical, but circular is very simple, elliptical is a bit more complicated. But it's independent of the strength of the cosine for weight cosines. Yes, yes.

364
00:30:48.700 --> 00:30:56.559
Rm 330: Because you just… you just compute this area, you expand it in powers of T perk, and then you imagine the coefficient of t plus.

365
00:30:58.740 --> 00:31:02.319
Rm 330: And what selects the angle is stationarity of Moon's quantity D.

366
00:31:02.690 --> 00:31:04.170
Rm 330: of this area.

367
00:31:04.390 --> 00:31:05.529
Rm 330: I see that.

368
00:31:10.270 --> 00:31:11.540
Rm 330: Anyway, so…

369
00:31:11.810 --> 00:31:24.109
Rm 330: you can go ahead and, you know, solve the… oh, I didn't write it down, the Bolton equation. Anyway, I removed that slide. It just comes from solving the Boltman equation, which we have done in this paper in great detail, if you want to read about it.

370
00:31:25.570 --> 00:31:29.819
Rm 330: And we also account for isotropic and quasi-particle residue around.

371
00:31:33.240 --> 00:31:37.580
Rm 330: Anyway, okay, so… So now I want to…

372
00:31:37.770 --> 00:31:44.040
Rm 330: So I've given you a toy model of FL star, and I've given you some evidence… and the toy model is useless.

373
00:31:44.210 --> 00:31:51.889
Rm 330: Exactly, tells you the right Fermi surface area. That's what we measured. But we want to do much better. We want an actual theory.

374
00:31:55.570 --> 00:32:02.720
Rm 330: And for an actual theory, we need an actual spin and a good knock this RVD state that I wrote down, which is showing very far from the truth.

375
00:32:03.160 --> 00:32:08.380
Rm 330: And so, you know… So I now want to talk about…

376
00:32:08.660 --> 00:32:16.359
Rm 330: put some more meat in this type of volatility picture. And really what's made that possible, at least in our work.

377
00:32:16.580 --> 00:32:19.820
Rm 330: Is that there's been now a much deeper, better understanding.

378
00:32:19.940 --> 00:32:23.040
Rm 330: Of possible spin liquors on the square dice.

379
00:32:23.830 --> 00:32:29.500
Rm 330: You know, when all this started in the 80s, there was no guitar, there was… Nothing,

380
00:32:29.670 --> 00:32:33.400
Rm 330: Now, there are many solvable models, there's a huge amount of progress.

381
00:32:33.510 --> 00:32:38.290
Rm 330: In numerical work, Also, field theory, which is what I'll discuss.

382
00:32:38.530 --> 00:32:41.160
Rm 330: And plus…

383
00:32:41.330 --> 00:32:47.609
Rm 330: And also an understanding, not just on other lattices, like Canyon, but also on the square lattice.

384
00:32:49.480 --> 00:32:51.919
Rm 330: So let me just very quickly review.

385
00:32:52.310 --> 00:32:54.030
Rm 330: 30 plus years of work.

386
00:32:54.830 --> 00:32:59.350
Rm 330: Alright, so… You imagine, you know, so one of the first papers

387
00:32:59.640 --> 00:33:05.620
Rm 330: was this paper by Arubus and Orbach, who said, we take your sprints, and…

388
00:33:06.330 --> 00:33:10.200
Rm 330: Write them in terms of this sugar boson. These are spinons, which are bosons.

389
00:33:10.350 --> 00:33:15.740
Rm 330: And take some mean field theory with a pair, and then you get a state that doesn't break any symmetry.

390
00:33:15.850 --> 00:33:19.039
Rm 330: Which has a gap, so there's a stink gap state.

391
00:33:19.900 --> 00:33:26.780
Rm 330: Okay, so shortly afterwards, and there's some place from this, and they lose the name order, as you'd say, grant up the frustration.

392
00:33:27.870 --> 00:33:31.240
Rm 330: But then, in work with Nick Reed.

393
00:33:31.380 --> 00:33:36.389
Rm 330: What we showed was look at the fluctuations about the saddle point of a reverse and Arava.

394
00:33:36.890 --> 00:33:40.379
Rm 330: We said, well, there is a view on gauge symmetry associated with this.

395
00:33:40.580 --> 00:33:42.710
Rm 330: So really, how do you take your bosons.

396
00:33:43.100 --> 00:33:45.839
Rm 330: and couple them to the C1 gauge field.

397
00:33:46.570 --> 00:33:50.780
Rm 330: And at low energies, you get this field theory called the CP1 field theory.

398
00:33:51.370 --> 00:33:54.289
Rm 330: And then they're also here to worry about the anomalies.

399
00:33:54.420 --> 00:33:59.769
Rm 330: In this case, the anomalies appear as berry phases of monopole operators.

400
00:34:00.160 --> 00:34:05.819
Rm 330: And… Then we figured out what the consequence of these anomalies was.

401
00:34:05.980 --> 00:34:11.590
Rm 330: That this state, in fact, is actually confining, and has this valence bond solid.

402
00:34:11.699 --> 00:34:13.230
Rm 330: type broken synergy.

403
00:34:14.840 --> 00:34:15.800
Rm 330: Alright.

404
00:34:16.370 --> 00:34:24.900
Rm 330: And then somewhat later, people turned their attention to this phase transition, and that's been identified as a possible deep and fine

405
00:34:25.100 --> 00:34:27.370
Rm 330: Point, critical point. Okay.

406
00:34:27.710 --> 00:34:32.040
Rm 330: So this took a while for all of this to work out and start to get understood.

407
00:34:32.600 --> 00:34:35.620
Rm 330: But there was another parallel development.

408
00:34:35.929 --> 00:34:40.489
Rm 330: Where people, instead of starting with boson expunions,

409
00:34:40.659 --> 00:34:42.760
Rm 330: Oh, I should say this whole picture.

410
00:34:42.900 --> 00:34:45.059
Rm 330: Of a possible critical point.

411
00:34:45.310 --> 00:34:52.010
Rm 330: And the nail stage in BBS is consistent in many, many numerical works for the J1, J2 model.

412
00:34:52.500 --> 00:34:54.590
Rm 330: This point is around 0.5.

413
00:34:55.400 --> 00:35:02.460
Rm 330: Okay, so… You know, things are working, but this seems to have no connection to the cuperates.

414
00:35:03.110 --> 00:35:05.329
Rm 330: I certainly thought that for a while.

415
00:35:06.600 --> 00:35:09.280
Rm 330: Okay, nice. Hey.

416
00:35:09.620 --> 00:35:17.009
Rm 330: So there was another parallel development where people represented the spins in terms of fermions, fermionic spinons.

417
00:35:17.580 --> 00:35:24.590
Rm 330: And in this case, the optimal state, several point, which is a spin liquid, turns out to be this pi flux state.

418
00:35:25.100 --> 00:35:33.140
Rm 330: There were others, but this is actually the one that I need to focus on, we now understand, as I explained in a minute.

419
00:35:33.590 --> 00:35:41.719
Rm 330: So these EIGs is fixed numbers, and this is the effective Hamiltonian of this All these feelings.

420
00:35:42.570 --> 00:35:46.120
Rm 330: So this theory actually has an SU2 gauge invariance.

421
00:35:46.660 --> 00:35:51.010
Rm 330: So you have to… if you're going to look at fluctuations, you have to…

422
00:35:51.230 --> 00:35:54.410
Rm 330: look at fluctuations of an SC2 gauge field.

423
00:35:54.720 --> 00:36:00.909
Rm 330: And the spin-ons in the continuum have a… Dirac spectrum, just like graphene.

424
00:36:01.140 --> 00:36:08.840
Rm 330: And then here, in fact, the pi flux doubles in itself, so again, you have two valleys of Dirac spinons.

425
00:36:09.040 --> 00:36:15.589
Rm 330: But these are, unlike graphene, these spinels don't carry charge, they only carry spin. And they're also coupled to the SC2 gauge.

426
00:36:17.430 --> 00:36:21.410
Rm 330: And now, of course, this SC2 gauge, you know, this is almost like QCD.

427
00:36:21.800 --> 00:36:26.820
Rm 330: your two dimensions, the two families of quartz coupled with SC2.

428
00:36:27.030 --> 00:36:38.550
Rm 330: Whereas in QCD, you have three dimensions, three families. So easy to remember, just take 3 to 2, and it's exactly the same. And we know in QCD,

429
00:36:38.690 --> 00:36:43.179
Rm 330: mass SQCD, is confined, and you get variants.

430
00:36:43.640 --> 00:36:46.240
Rm 330: So what about here? There's this theory you can find.

431
00:36:46.920 --> 00:36:48.060
Rm 330: And…

432
00:36:48.480 --> 00:36:54.660
Rm 330: So, the present understanding is that, yes, it does, except possibly at a critical point, where you have a deconfined

433
00:36:54.900 --> 00:36:59.600
Rm 330: The exact type, beautiful state.

434
00:37:00.910 --> 00:37:11.469
Rm 330: So the confining state, very beautifully, cannot be exactly the same states that you obtain in the bosonic spin-on theory. The nail state and the very small solid.

435
00:37:11.710 --> 00:37:21.539
Rm 330: And so there's a whole different way of obtaining exactly the same state, and become consistent with lots of generics, starting from this fermionic spin on description.

436
00:37:21.860 --> 00:37:28.510
Rm 330: So there's this, duality or triability diagram you can draw, which I won't go into any detail.

437
00:37:28.700 --> 00:37:31.529
Rm 330: And that there seems to be, just to the point

438
00:37:31.940 --> 00:37:39.969
Rm 330: Where the nail state disappears and frustrated anti for a magnet, a nearly critical state.

439
00:37:40.390 --> 00:37:43.430
Rm 330: Which has different… which is strongly coupled, unfortunately.

440
00:37:44.740 --> 00:37:50.250
Rm 330: It's not like some simple theromagnet where you can understand things very exactly.

441
00:37:50.710 --> 00:37:57.579
Rm 330: But, it has different descriptions depending on which particular Approximation you want to make.

442
00:37:58.100 --> 00:38:03.890
Rm 330: And there's been a lot of beautiful work, especially this work by Yin Chen Hay.

443
00:38:04.140 --> 00:38:05.760
Rm 330: Where is it? Here.

444
00:38:05.990 --> 00:38:07.890
Rm 330: On, here, this one.

445
00:38:08.150 --> 00:38:17.949
Rm 330: On the fuzzy sphere, that has really given a lot of confirmation of this basic Okay, so now…

446
00:38:18.290 --> 00:38:20.020
Rm 330: We want to dope this thing.

447
00:38:20.360 --> 00:38:28.429
Rm 330: So the point of view we're going to take is that, for mysterious reasons, when you dope the antiferromagnet, and you lose the antiferromagnetic order.

448
00:38:28.740 --> 00:38:34.069
Rm 330: Just like in this system, when you lose the antiferromagnetic order, you enter this nearly critical state.

449
00:38:34.220 --> 00:38:38.449
Rm 330: So let's assume you enter that nearly created state, and you dope.

450
00:38:38.800 --> 00:38:41.149
Rm 330: And what can you say about the charger sector?

451
00:38:43.040 --> 00:38:45.349
Rm 330: Alright, so I'm gonna do this first.

452
00:38:45.600 --> 00:38:50.539
Rm 330: just… by using, kind of, Landau-Ginsberg theory.

453
00:38:50.670 --> 00:38:57.609
Rm 330: you know, When Landau Ginsburg proposed it to use superconductivity, they just used some very general arguments.

454
00:38:57.870 --> 00:38:59.829
Rm 330: They didn't have any microscopics.

455
00:39:00.230 --> 00:39:03.179
Rm 330: And then Gorkov gave a microscopic derivation.

456
00:39:03.860 --> 00:39:06.320
Rm 330: So I first have to land Orginsburg.

457
00:39:06.580 --> 00:39:09.280
Rm 330: And then I'll do the analog door.

458
00:39:09.480 --> 00:39:11.050
Rm 330: At the end of my talk.

459
00:39:11.440 --> 00:39:13.130
Rm 330: I'm gonna do not touch.

460
00:39:13.850 --> 00:39:15.700
Rm 330: 2.30 after that, okay.

461
00:39:16.020 --> 00:39:18.400
Rm 330: So I probably won't get to the logoff part.

462
00:39:20.050 --> 00:39:23.950
Rm 330: So here, the difference here, I mean, the idea is actually very similar.

463
00:39:24.260 --> 00:39:27.760
Rm 330: what it ends up getting looks like? Well, it populates an order parameter.

464
00:39:28.090 --> 00:39:34.689
Rm 330: And look at its transformation of the symmetries, and write down the most general free energy consistent with those symmetries.

465
00:39:34.980 --> 00:39:42.759
Rm 330: We're going to do exactly the same, except that the order parameter also carries the gauge charge. So I also have to include the gauge field.

466
00:39:42.960 --> 00:39:49.510
Rm 330: And worry about… The fate under gaze transformation, too.

467
00:39:50.180 --> 00:39:54.440
Rm 330: Is this at all similar to a two-component superconductor? No, no.

468
00:39:54.650 --> 00:39:56.810
Rm 330: Even though… It's…

469
00:39:57.000 --> 00:40:01.940
Rm 330: So what you get here, what are called projected symmetries. In other words, when you have a gauge symmetry.

470
00:40:02.440 --> 00:40:08.149
Rm 330: Now, when you have a system without gasey, then you do some translation, the system has to return to itself.

471
00:40:08.380 --> 00:40:14.160
Rm 330: When you have a gauge symmetry, when you do a translation, it has to return to itself up to a gauge transformation.

472
00:40:14.710 --> 00:40:20.750
Rm 330: And that's the entire game is keeping track of those gauge constant that you have to do to restore sync.

473
00:40:21.210 --> 00:40:23.689
Rm 330: I mean, you're very familiar with this inland levels.

474
00:40:23.900 --> 00:40:31.000
Rm 330: Exactly the same kind of thing here, but there's no magnetic field, but there is still this emergency transformation track.

475
00:40:31.900 --> 00:40:33.290
Rm 330: So we all the rest of it.

476
00:40:33.790 --> 00:40:37.620
Rm 330: So, in fact, let's start with the… Oh.

477
00:40:38.200 --> 00:40:42.169
Rm 330: With this… this theory, which is the 5-flux lean-field state.

478
00:40:42.320 --> 00:40:48.379
Rm 330: You can even add, you know, this… for example, this thing… Has pi flux.

479
00:40:48.510 --> 00:40:53.509
Rm 330: And what this means is that for these spin-ons, TX and TY anti-pinute.

480
00:40:54.420 --> 00:40:59.319
Rm 330: And that's always been not true for any observable DMs and device should commute.

481
00:40:59.500 --> 00:41:02.119
Rm 330: So there are a lot of intellectuals, because

482
00:41:02.680 --> 00:41:10.750
Rm 330: You're talking about an object that has a gauge charge. They cannot enter commute for something that is gauge neutral.

483
00:41:11.110 --> 00:41:15.919
Rm 330: The only anti-camute was something that carries a gauge chart. In this case, the SC2 gauge chart.

484
00:41:16.150 --> 00:41:24.739
Rm 330: So in fact, you have to keep track of what's called the projected symmetry group, what are the gauge transformation required for… under all symmetries?

485
00:41:25.220 --> 00:41:26.969
Rm 330: And so, for the spin-ons.

486
00:41:27.210 --> 00:41:38.719
Rm 330: Again, we can make a table of that. These are translations and reflections and time reversal. These are the transformations required to preserve the full symmetry of the underlying areas.

487
00:41:38.920 --> 00:41:41.219
Rm 330: So, if I had a lattice with very curvature.

488
00:41:41.480 --> 00:41:49.520
Rm 330: I would also have similar features to the translation operators, if I were to embed them in real space. So I have two sites per cell, I insert a Haldane flux.

489
00:41:49.560 --> 00:42:02.319
Rm 330: I have exactly this property here. Well, I have a system… I have a unit cell with a floods, right? So if I make them… Your Hamiltonian is strictly translation invariant. What? Your Hamiltonian is strictly translation invariant.

490
00:42:02.320 --> 00:42:10.069
Rm 330: That you start. The holiday Hamiltonian has complete translational symmetry of the honeypole matter. Right, but I do… You don't need any gauge transformation to undo it.

491
00:42:10.310 --> 00:42:12.979
Rm 330: Right. This is only important here, it's really important that…

492
00:42:13.220 --> 00:42:16.089
Rm 330: We're not talking about… forgive all objects.

493
00:42:16.260 --> 00:42:23.249
Rm 330: There are any… that cannot be created by a local operator. They're fractionalized objects, so they carry an emergency charge.

494
00:42:23.400 --> 00:42:27.360
Rm 330: These are all different ways of saying the same thing.

495
00:42:27.600 --> 00:42:35.199
Rm 330: So the spin-on… Not a physical, though. Right. So it's allowed to have some transformation.

496
00:42:35.850 --> 00:42:38.840
Rm 330: Provided all gates and observers don't.

497
00:42:39.050 --> 00:42:56.329
Rm 330: This is what you keep in for… so what you do, that in fact, leads me to the next point. The DXTY plus minus TYTX, is that acting on all the states of the helper space, or only acting on the ground state? This is the one spin-on state, yeah. On the one spin-on state? Yeah.

498
00:42:56.510 --> 00:43:00.570
Rm 330: The exact once-in-one state, yeah. It's not a popular Lagrams state.

499
00:43:02.910 --> 00:43:07.969
Rm 330: I mean, strictly speaking, so in reality, you cannot create a once-in-one state on its own.

500
00:43:08.120 --> 00:43:10.769
Rm 330: So you had to take the sprinkles really far apart.

501
00:43:10.970 --> 00:43:23.010
Rm 330: And then doing these operations, and… you know, so that's… that's the subtlety that people now figure out how to do it rigorously, anyway. But operation is very simple.

502
00:43:23.270 --> 00:43:27.580
Rm 330: You just take one spin on in this region, and you just look at how it transforms.

503
00:43:28.830 --> 00:43:33.489
Rm 330: So really, in the end, that's all you need. So now I want to…

504
00:43:33.770 --> 00:43:37.079
Rm 330: To have charge fluctuations, so there has to be some boson.

505
00:43:37.240 --> 00:43:40.680
Rm 330: Which, when fused with the left spin-on, gives an electron.

506
00:43:40.980 --> 00:43:43.250
Rm 330: And the electron better be…

507
00:43:43.560 --> 00:43:50.430
Rm 330: invariant. It cannot pick up any extra phases under these terms. Electrons are physically absorbed.

508
00:43:51.080 --> 00:43:52.160
Rm 330: So, since…

509
00:43:52.530 --> 00:44:01.399
Rm 330: Spin on times charge-on is an electron. I know spin-on, I know charge-on. I'm sorry, I know spin-on and electron. I can deduce charge on.

510
00:44:01.860 --> 00:44:04.490
Rm 330: That's all there is to it, and that gives me the second call.

511
00:44:05.480 --> 00:44:08.709
Rm 330: Alright, so there is some… degree of freedom.

512
00:44:09.220 --> 00:44:12.940
Rm 330: It's either condensed, or fluctuating, or tonally fluctuating.

513
00:44:13.130 --> 00:44:18.889
Rm 330: which must transform in this way, which carried charge E, and is also fundamental in the SC2 gate charge.

514
00:44:19.760 --> 00:44:24.049
Rm 330: So now you take this boson, you write down different possible.

515
00:44:25.800 --> 00:44:29.359
Rm 330: Different possible gauge invariant objects.

516
00:44:30.360 --> 00:44:35.860
Rm 330: So, for example, you could, write on this object, on any bond.

517
00:44:36.290 --> 00:44:39.799
Rm 330: And then you can see, by studying this table a lot.

518
00:44:40.000 --> 00:44:44.080
Rm 330: That the transformation of this object is the same as this object.

519
00:44:44.350 --> 00:44:46.149
Rm 330: Under all synergies.

520
00:44:46.700 --> 00:44:54.129
Rm 330: Which is just the pairing object, actually. And similarly for the side chart density. So what… so this is really the main…

521
00:44:54.520 --> 00:44:56.199
Rm 330: I'll put a lot of this.

522
00:44:56.610 --> 00:45:03.489
Rm 330: given any configuration of B, I can, by taking the different bilinears, I can see which symmetry is broken.

523
00:45:04.040 --> 00:45:06.380
Rm 330: Because if I get some condensate of beef.

524
00:45:06.740 --> 00:45:12.000
Rm 330: It might be that the pairing is non-zero, or the bond density is not uniform.

525
00:45:12.310 --> 00:45:18.769
Rm 330: And that tells me what's wrong. And that's the gauge and fair answer. Different people will do the calculation different ways.

526
00:45:20.040 --> 00:45:24.929
Rm 330: All right. And then the next step in, Landau theory is to write down some

527
00:45:25.200 --> 00:45:27.739
Rm 330: Simple free energy inherent under everything.

528
00:45:27.940 --> 00:45:33.849
Rm 330: So this is what we did. We just took out a quarter term, nearest neighbor, and…

529
00:45:34.040 --> 00:45:37.019
Rm 330: If you take only nearest neighbor terms, you minimize it.

530
00:45:37.170 --> 00:45:41.590
Rm 330: This is the phase diagram you're getting. So, here, this is just mean field theory.

531
00:45:41.880 --> 00:45:44.880
Rm 330: Like in Landon Ginsburg, there's a schematic R.

532
00:45:45.860 --> 00:45:50.229
Rm 330: And… so, when R is large and positive, forget about B.

533
00:45:50.600 --> 00:45:57.359
Rm 330: So if I plot a phase diagram as a function of R, and R is large and positive, B is just 0 in greenfield theory.

534
00:45:57.850 --> 00:46:00.620
Rm 330: then what is the theory? The theory is just a spin-offs.

535
00:46:00.810 --> 00:46:03.179
Rm 330: I've already told you what the spinons do.

536
00:46:03.660 --> 00:46:06.480
Rm 330: They form an air state, or the air is born solid.

537
00:46:06.920 --> 00:46:09.300
Rm 330: Yup.

538
00:46:09.810 --> 00:46:13.439
Rm 330: Okay, this is it. How filling, when you evaluate how filling.

539
00:46:13.570 --> 00:46:16.360
Rm 330: B was never allowed to be 0 because it has to.

540
00:46:16.630 --> 00:46:20.479
Rm 330: But anyway, so this is a plausible state, at least at halfway.

541
00:46:21.050 --> 00:46:24.289
Rm 330: So far, I'm just intro terminology.

542
00:46:24.430 --> 00:46:26.700
Rm 330: What do you get at V less than zero?

543
00:46:26.800 --> 00:46:29.939
Rm 330: Well, in the simplest model, you get 3 states, amazingly.

544
00:46:30.570 --> 00:46:36.150
Rm 330: One of them is a D-Wave superconductor. This is not an S-wave, it comes out, it has D wave.

545
00:46:36.500 --> 00:46:42.089
Rm 330: And that's precisely coming from the pi flux. So this is a…

546
00:46:42.220 --> 00:46:49.030
Rm 330: This connection between the pi flux and the D wave superconductor goes back to Gabby and many other people in the early… late 80s.

547
00:46:49.230 --> 00:46:50.529
Rm 330: This is like a…

548
00:46:50.700 --> 00:46:57.510
Rm 330: You know, let's say a modern way, a very systematic way of deriving it, in a morally independent way.

549
00:46:58.980 --> 00:47:11.039
Rm 330: There are also other states. In fact, this stripe state, this is some staggered flux state, or a T-density state, it's called. These are all possibilities in this land of functional.

550
00:47:11.460 --> 00:47:19.209
Rm 330: So there's a very good set of possibilities. When you put second-name interactions, you can even get charge density with fewer 4,

551
00:47:19.530 --> 00:47:25.310
Rm 330: And also this D-Wave superconductor. So we're going to now sit over here.

552
00:47:25.690 --> 00:47:29.379
Rm 330: And try to do a better theory, more than just…

553
00:47:29.660 --> 00:47:38.930
Rm 330: Mean field theory. What is… what is the U? I didn't… didn't catch the U. A U is the… oh, it's the gauge field, it's not the Hubbard U, it's the SU2 gauge field.

554
00:47:39.050 --> 00:47:42.689
Rm 330: So, yeah, you have to minimize back to YouTube.

555
00:47:42.870 --> 00:47:48.350
Rm 330: So there is this Maxwell term with capital large. So generally, it tends to prefer U equals 1.

556
00:47:49.040 --> 00:47:52.179
Rm 330: But when you do fluctuations, you have to include fluctuations.

557
00:47:53.300 --> 00:47:55.799
Rm 330: And the speedruns have been interminated.

558
00:47:56.460 --> 00:48:05.649
Rm 330: Well, they're there, but yes, for now, I'm just doing the simplest thing. We've done a lot more with spinos, but I don't have time to get there.

559
00:48:07.180 --> 00:48:16.760
Rm 330: So, for now, yes, for the next thing I'll talk about, let's imagine you integrated spin-ons, and the effect of the spin-on is absorbed in all of these coupling constants, which we don't know anyway.

560
00:48:17.160 --> 00:48:20.570
Rm 330: This is exactly what worked me online now, Ginsburg.

561
00:48:20.960 --> 00:48:21.830
Rm 330: Let's say.

562
00:48:23.870 --> 00:48:27.240
Rm 330: So that Lionau Ginsburg is okay at finite temperature.

563
00:48:27.680 --> 00:48:30.190
Rm 330: And so now we're actually going to look at finance efforts.

564
00:48:31.450 --> 00:48:32.860
Rm 330: So, what do we do?

565
00:48:34.440 --> 00:48:37.690
Rm 330: So this is what… this is the Monte Carlo simulation we did.

566
00:48:38.210 --> 00:48:40.690
Rm 330: We just took this action.

567
00:48:41.550 --> 00:48:45.840
Rm 330: And look at thermal fluctuations, that's it, to begin with.

568
00:48:46.030 --> 00:48:47.789
Rm 330: So we have B and U.

569
00:48:48.080 --> 00:48:54.680
Rm 330: So we chose the parameters of B and U so that the ground state at zero temperature

570
00:48:54.850 --> 00:48:56.680
Rm 330: It's just a DX supermarket.

571
00:48:59.350 --> 00:49:00.909
Rm 330: Okay, and then we…

572
00:49:01.020 --> 00:49:05.640
Rm 330: the systematic all the simulation, including both P. It is important to include both P and U.

573
00:49:05.760 --> 00:49:07.999
Rm 330: I've only come with fluctuations.

574
00:49:08.950 --> 00:49:11.799
Rm 330: So this is a two-dimensional lattice gauge theory.

575
00:49:12.270 --> 00:49:18.100
Rm 330: with us, Kingsfield, and, SC2 gauge field.

576
00:49:18.700 --> 00:49:24.179
Rm 330: So, much simpler than what people do in particle physics, but more complicated action nonetheless.

577
00:49:25.370 --> 00:49:32.400
Rm 330: Because the flux gives you extra… the flux acting on the B,

578
00:49:32.640 --> 00:49:35.419
Rm 330: That gives you all these competing ground states.

579
00:49:39.010 --> 00:49:45.129
Rm 330: So, here's a simulation where we are actually measuring some physical quantities, gauging their quantities.

580
00:49:45.240 --> 00:49:47.629
Rm 330: Here's the phase of the pairing altitude.

581
00:49:48.010 --> 00:49:52.680
Rm 330: There's a snapshot. And you see very beautifully, there are vortices here.

582
00:49:53.740 --> 00:49:58.720
Rm 330: And the vortices… Have a flux of exactly 2 pi.

583
00:50:00.570 --> 00:50:10.360
Rm 330: For the pairing autoparameter. Which means the physical… since the pairing autoparameter is charged 2, yeah, what is the flux H over… physical flux, H over 2E?

584
00:50:11.100 --> 00:50:17.560
Rm 330: Now, this is significant, because The boson that we have, Has only charity.

585
00:50:18.380 --> 00:50:23.760
Rm 330: So, if I did this calculation without ASC2GH field, I would get policies which are twice as large.

586
00:50:24.280 --> 00:50:28.780
Rm 330: But here, because of the acetyl gauge field, there's a defining effect.

587
00:50:28.960 --> 00:50:35.230
Rm 330: And the physical order parameter, and the physical vortices are exactly what you get. So this is a… in the sense.

588
00:50:35.790 --> 00:50:40.579
Rm 330: Yeah, the answers are gauge is actually crucial to get the right superconductor and the right vortices.

589
00:50:41.390 --> 00:50:47.760
Rm 330: Even more interesting is if you look at every one of these vortices, and you look at the bond density, for example.

590
00:50:48.050 --> 00:50:51.019
Rm 330: You see this pattern? You can zoom in. This is what you see.

591
00:50:51.610 --> 00:50:54.029
Rm 330: So, at the core of each vortex.

592
00:50:54.730 --> 00:51:00.980
Rm 330: The other photo parameters appear, very naturally, not by tuning some Thank you, B&G.

593
00:51:01.310 --> 00:51:03.209
Rm 330: You know, the boson…

594
00:51:03.450 --> 00:51:11.259
Rm 330: Really, it's the same boson that's leading to the charge density wave that's leading to this, there's just different components of this fractionalized outer prime.

595
00:51:12.230 --> 00:51:23.019
Rm 330: And, you know, that's supposed to be similar, but at least qualitatively than what's seen in many experiments with the antidote for disease using STN.

596
00:51:24.460 --> 00:51:28.500
Rm 330: And then you also see a beautiful costless dollars transition.

597
00:51:28.680 --> 00:51:32.249
Rm 330: Again, associated with flux H over 2E.

598
00:51:34.880 --> 00:51:35.930
Rm 330: Okay.

599
00:51:36.740 --> 00:51:39.910
Rm 330: So… I have 4 minutes left.

600
00:51:40.090 --> 00:51:41.840
Rm 330: Is that about right?

601
00:51:42.230 --> 00:51:44.030
Rm 330: Any questions on that part?

602
00:51:45.000 --> 00:51:45.900
Rm 330: Yes.

603
00:51:46.170 --> 00:52:01.160
Rm 330: Super… this is… the Hitchfield's in the fundamental representation. Correct, correct, yes. So, I think models like this generally have either a smooth crossover or a first-order transition.

604
00:52:01.480 --> 00:52:09.300
Rm 330: They don't typically have second-order returns. What is the thorough transition at finite temperature? It says this is just a costless, Thomless transition.

605
00:52:09.520 --> 00:52:24.820
Rm 330: There's only one thing happening at this transition is a quality long-range order of the pairing amplitude, nothing else. So in terms of universalities, nothing more nor less than cost. It's caged. Huh? It's caged. Oh, there's also a global U1 symmetry that's…

606
00:52:24.940 --> 00:52:31.209
Rm 330: So the Higgs field carries both. It's a fundamental MSC2, and it also carries a global U.

607
00:52:32.210 --> 00:52:35.990
Rm 330: That's the one that's causing the foundation. Oh, I see. Yeah.

608
00:52:36.750 --> 00:52:41.740
Rm 330: SU2 cross U1, it's really, again, strikingly similar to…

609
00:52:42.300 --> 00:52:58.009
Rm 330: And the CO2 gauge fields are confining. Yes, yes. Always. Yes. They don't change as well. Well, except they're just… There's nothing confined. Well, there, you know, so I haven't talked about it, but they can be a deconfined critical point.

610
00:52:58.030 --> 00:53:03.239
Rm 330: In here, between the nail phase and the superconductor.

611
00:53:03.370 --> 00:53:15.000
Rm 330: But it's a function of temperature. No, no, nothing. It's always the fire. But, presumably, you know, this is the next part, is how do you get the pockets? To get the pockets, you need some beacon fire.

612
00:53:16.230 --> 00:53:19.230
Rm 330: Well, those are associated with speakers. It is completely confining.

613
00:53:19.360 --> 00:53:23.410
Rm 330: Then I thought, why should I work with this? I think this worked with superconducting autofarameter.

614
00:53:24.030 --> 00:53:29.580
Rm 330: Which is reasonable as far as the autofund is concerned, but for the fermionic spectrum, it doesn't work.

615
00:53:29.740 --> 00:53:30.560
Rm 330: Yeah.

616
00:53:31.240 --> 00:53:38.109
Rm 330: I'll email you, I have to go, but… Okay, all right. Thanks, Tom. All right, so let me just…

617
00:53:38.470 --> 00:53:45.180
Rm 330: zip through the very last part, sorry. And now, so now to do something like Gorkov, I have to actually write down a moral.

618
00:53:45.300 --> 00:53:47.259
Rm 330: Not just use symmetries.

619
00:53:47.500 --> 00:53:50.540
Rm 330: And that's, you know, been very, very tricky.

620
00:53:50.650 --> 00:53:57.399
Rm 330: How do you write down a Hamiltonian whose ground state is this ethyl star state? I have to put the electrons back in.

621
00:53:58.140 --> 00:54:02.519
Rm 330: So this was a problem I've been worrying about for decades, really.

622
00:54:02.840 --> 00:54:06.310
Rm 330: And, I think sort of a breakthrough came

623
00:54:06.540 --> 00:54:10.569
Rm 330: idea from Yahoo Yi Zhang, who's now faculty at Johns Hopkins.

624
00:54:10.910 --> 00:54:14.079
Rm 330: Where he introduced the idea of ancillors.

625
00:54:15.070 --> 00:54:18.859
Rm 330: So, we've… And the basic idea is in this picture.

626
00:54:19.360 --> 00:54:20.490
Rm 330: Oh.

627
00:54:21.230 --> 00:54:23.500
Rm 330: So, we want to understand the Hubble model.

628
00:54:24.680 --> 00:54:26.729
Rm 330: with density 1 plus P.

629
00:54:27.210 --> 00:54:30.180
Rm 330: I'm just going to put some spectator answers.

630
00:54:30.290 --> 00:54:39.470
Rm 330: which form this gapped, trivial state. Very important that you have a gapped ground, trivial ground state. It can't have any anomaly of its own.

631
00:54:39.570 --> 00:54:41.270
Rm 330: That'll just change the whole problem.

632
00:54:41.640 --> 00:54:44.629
Rm 330: So I have to… two layers of spin, not one layer.

633
00:54:45.090 --> 00:54:49.400
Rm 330: Many people have put one layer and just give you wrong answers. You have to have two.

634
00:54:50.760 --> 00:54:58.019
Rm 330: Okay, so now there's a simple canonical transformation you can do between two decoupled systems, with the Hubbard U here.

635
00:54:58.650 --> 00:55:02.400
Rm 330: To this system, At least at Large API work.

636
00:55:03.040 --> 00:55:05.450
Rm 330: It's… it's just… it's the same.

637
00:55:05.590 --> 00:55:07.659
Rm 330: Now there's a coupling JK.

638
00:55:07.800 --> 00:55:10.059
Rm 330: But these electrons here are free.

639
00:55:10.410 --> 00:55:11.479
Rm 330: Or holds.

640
00:55:12.130 --> 00:55:19.410
Rm 330: And the U, this is the physical view now, now it's the Hubbard view. Sorry for the excessive views of U.

641
00:55:19.660 --> 00:55:32.390
Rm 330: is JK squared over J perp. You can just do this, it's the conventional free focal transformation, and you can see that this model, at least at large JFERP, is completely equivalent to this model.

642
00:55:34.020 --> 00:55:46.030
Rm 330: So now here, now the advantage of this model, it gives you more handles, and a different way to think about it, and to use all the insights that have been gained over the last decades on the condo model, because I've written it at, like, a

643
00:55:46.160 --> 00:55:50.149
Rm 330: Sort of like a condo model with two layers of what it becomes.

644
00:55:51.110 --> 00:55:55.640
Rm 330: So now the idea is that the Jay Condo initially is supposed to be weak.

645
00:55:56.190 --> 00:56:02.150
Rm 330: We know what condo couplings, especially anti-ferromagnetic condo couplings, always want to do, is run to infinity.

646
00:56:02.440 --> 00:56:07.810
Rm 330: So let's imagine that, for mysterious reasons, JK has become large.

647
00:56:08.160 --> 00:56:12.050
Rm 330: then what is the ground state of this particular model when JP is very large?

648
00:56:12.230 --> 00:56:14.399
Rm 330: Well, the ground state is shown here.

649
00:56:14.710 --> 00:56:17.149
Rm 330: The top two layers, just a condo lattice.

650
00:56:17.340 --> 00:56:23.190
Rm 330: And they're going to form the heavy Fermi liquid state, which counts both the spins and the electrons. That's what

651
00:56:23.420 --> 00:56:29.500
Rm 330: You know, that appeared in… I guess if he's common, and… Kane, no.

652
00:56:30.370 --> 00:56:35.880
Rm 330: Millis and Lee and various other papers already in the… Late 80s.

653
00:56:36.130 --> 00:56:38.309
Rm 330: I haven't seen in many experiments.

654
00:56:38.680 --> 00:56:45.540
Rm 330: So, in that case, the Fermi surface counts both layers. But here, what is the size?

655
00:56:45.690 --> 00:56:48.120
Rm 330: Well, 1 plus P is the density here.

656
00:56:48.370 --> 00:56:50.360
Rm 330: One is the density of spins.

657
00:56:50.580 --> 00:56:56.820
Rm 330: So that's… everything's Module 2, so it's peace. In fact, you get your pockets for free right away.

658
00:56:57.530 --> 00:57:03.790
Rm 330: And then Oshikawa says, If you have violating the latent value, you better have a spin liquid.

659
00:57:04.050 --> 00:57:13.799
Rm 330: And that's exactly what this theory tells you automatically, so it's like Oshikawa for idiots, tells you there's… it has a spin liquid. This must form a spin liquid, otherwise it's not possible.

660
00:57:15.520 --> 00:57:17.450
Rm 330: Okay, so that's the state.

661
00:57:17.630 --> 00:57:22.759
Rm 330: And now you can do a gauge theory with the usual bells and whistles of this state.

662
00:57:22.900 --> 00:57:31.900
Rm 330: And you get some… since I'm out of time, you get some complicated Hamiltonian, where the field B that I've been talking about is just the Hubbard's astronomicity coupling of J perp.

663
00:57:32.090 --> 00:57:37.060
Rm 330: And then you can… you condense 5 to get the heaviest from the liquid state.

664
00:57:37.300 --> 00:57:38.609
Rm 330: And, and then you…

665
00:57:39.050 --> 00:57:44.749
Rm 330: Write down some… in the background of B and U, you write down some theory for the fermions.

666
00:57:46.100 --> 00:57:54.199
Rm 330: Okay. Sorry, this is… I'll give you some references at the end. And so now we… we one-up the whole thing.

667
00:57:54.530 --> 00:57:56.439
Rm 330: You go back to this theory.

668
00:57:56.920 --> 00:58:01.720
Rm 330: When we simulated B and U, now this is the SC2 gauge field, sorry.

669
00:58:02.030 --> 00:58:08.269
Rm 330: And for each snapshot of B and U, we diagnose the Fermi Hammerton. So this is like the Von-Oppenheimer theory.

670
00:58:08.520 --> 00:58:11.490
Rm 330: The Higgs field and the gauge field are thermally fluctuating.

671
00:58:11.620 --> 00:58:14.459
Rm 330: For each snapshot, we're determining the spectrum.

672
00:58:15.690 --> 00:58:20.350
Rm 330: So when the gauge field is not fluctuating, you get these… they get the spin-ons.

673
00:58:21.540 --> 00:58:23.370
Rm 330: And you get the pockets.

674
00:58:23.810 --> 00:58:31.220
Rm 330: This is just the mean field theory of FL star. Now you put in these fluctuations, and you see the arcs that come out.

675
00:58:31.320 --> 00:58:34.299
Rm 330: Which hopefully are somewhat related to this.

676
00:58:34.990 --> 00:58:47.109
Rm 330: So that's kind of where we are. All right, so I will… oh, I think I'll skip this. This is something I… of particular interest to Gabby. How do you get anisotropic velocities? And it's complicated.

677
00:58:47.590 --> 00:59:02.250
Rm 330: You know, the various old problems with this idea from early work can all be resolved in this approach. How does the field be condensed? In which direction in a suitable space? That depends on your gait choice, or the…

678
00:59:02.450 --> 00:59:14.009
Rm 330: So if I do Affleck Marston, then it's got the B1 and B2. If I do cochlear, then it's just B1, things like that.

679
00:59:14.120 --> 00:59:18.710
Rm 330: This whole thing is gauging variant, doesn't matter which one you choose.

680
00:59:19.670 --> 00:59:26.030
Rm 330: I mean, the other order phases that you got, you had a zoo of order phases. What happens to that? Yeah, it's all…

681
00:59:27.350 --> 00:59:28.370
Rm 330: So…

682
00:59:29.880 --> 00:59:40.489
Rm 330: Yeah, the best way to think about it is you take the low energy spectrum of the B, and the B, since the B is moving 5 flux, it has two minima, a degenerate minima from the 5 flux.

683
00:59:40.760 --> 00:59:46.090
Rm 330: And so then… this… and VS2 components.

684
00:59:46.430 --> 00:59:52.239
Rm 330: complex, so you have a total of 8 fields, so there's, like, emerging SO8 symmetry.

685
00:59:52.500 --> 00:59:55.599
Rm 330: You mod it out by the gauge field, it gives you SO5.

686
00:59:55.760 --> 01:00:12.700
Rm 330: And so there are five auto parameters, and those turn out to be D-wave superconductor strikes and staggered flights. That was in our picture. And that's for the simplest model, and then when you put more complicated dispersion, you can get almost anything you want. Not anything, but a quite…

687
01:00:13.300 --> 01:00:18.920
Rm 330: Anyway, so then we just… Mentioned, very importantly, various people this work was done with.

688
01:00:19.110 --> 01:00:20.800
Rm 330: And Christos.

689
01:00:20.980 --> 01:00:28.550
Rm 330: only my student, and actually she was an undergraduate records, and if you remember her, she's now a postdoc at Caltech.

690
01:00:29.110 --> 01:00:32.909
Rm 330: Pietro, was my postdoc, and now…

691
01:00:33.050 --> 01:00:37.450
Rm 330: Junior, or some kind of junior group leader in Stuttgart and Nichsplatt.

692
01:00:37.750 --> 01:00:40.089
Rm 330: Alex is still my student.

693
01:00:40.380 --> 01:00:49.630
Rm 330: We'll be applying for jobs next year. Avishkar is now faculty in Bengaluru, and the Lattice Gate Theory work was done in collaboration with the Slattisgate Theory Group.

694
01:00:49.890 --> 01:01:00.269
Rm 330: In India. And here are various… These are review articles, and… the paper. So, thank you.

695
01:01:00.400 --> 01:01:01.100
Rm 330: Careful.

696
01:01:05.570 --> 01:01:21.200
Rm 330: This would be for a wonderful talk. Any questions, Jeff? On the, BKT transition. Yeah. It'd be time-pair to ask, does the TC come out as high at all? Like… It's very prohibited. All we checked was that the Nelson-Cost ratio was…

697
01:01:21.310 --> 01:01:28.180
Rm 330: It's not something… Everybody at the gauge 3 can actually give you a high TC, like, you know. But what we would like to do…

698
01:01:28.660 --> 01:01:43.500
Rm 330: And it goes up, this was already hard enough to do this as gates. We initially said, oh yeah, we know all the numbers, let's actually integrate out the fermions, compute the effective free energy, and then do Lattice Monte Carlo on the effective free energy obtained by

699
01:01:43.500 --> 01:01:52.490
Rm 330: Integrating out the fermions. Sort of like a carbonyl trick, right? Where you do DFT for each configuration, and then you do…

700
01:01:52.740 --> 01:01:53.920
Rm 330: Time evolution.

701
01:01:54.940 --> 01:02:13.899
Rm 330: That should be doable, but next step. We just first did a simpler thing that we did with just a phenomenological practice. When it comes down to his question, if you do mean field theory, you can get all the phases. Yes. And then you've done the fluctuations. What he wants to know is whether the fluctuations lower the DC or raise the DC.

702
01:02:14.600 --> 01:02:16.410
Rm 330: Relative to the mean field.

703
01:02:16.940 --> 01:02:36.289
Rm 330: Oh, I'm sure they lower it. So it's not that the TC comes from the gauge fluctuation. The gauge fluctuations actually lower what you put in mean fee. Well, so it's the costless… Well, it depends what you put in your Lagrant charge. I mean, he starts with some Lagrance. No, no, no, so the gauge fluctuation is actually good, because they can find the charity botan.

704
01:02:37.010 --> 01:02:39.899
Rm 330: the TC is coming from just phase fluctuation, so…

705
01:02:40.070 --> 01:02:44.310
Rm 330: In the end, this is not so different from the phase fluctuation scenario.

706
01:02:44.580 --> 01:02:51.809
Rm 330: Except, in the phase fluctuation scenario, there's really no way, to talk about the Fermion spectrum.

707
01:02:52.210 --> 01:02:55.180
Rm 330: Well, you know, at these higher temperatures.

708
01:02:55.300 --> 01:02:59.629
Rm 330: This gives you a way of… By fractionalizing the order parameter.

709
01:03:00.100 --> 01:03:04.349
Rm 330: The gauge field really becomes very important when I talk about the fermions.

710
01:03:04.680 --> 01:03:07.879
Rm 330: Well, the auto parameter itself is not that crucial.

711
01:03:08.830 --> 01:03:10.420
Rm 330: I wish I had this.

712
01:03:10.550 --> 01:03:20.739
Rm 330: You care about TC, right? Well, the question I had is about any SU2, you talked about U1 vortices for BKT. Do you have anything where SU… do you have some SU2 defects in the SUT theory that…

713
01:03:20.980 --> 01:03:22.460
Rm 330: Something not trivial?

714
01:03:22.850 --> 01:03:29.949
Rm 330: Not that I know, that's one of the advantages of SU2, there are no I want SU2 is zero, or something like that.

715
01:03:30.180 --> 01:03:32.220
Rm 330: It's just S3.

716
01:03:32.490 --> 01:03:42.290
Rm 330: Andress? Yeah. Can you go back to the Fermi arcs? So… Yes. So the story is basically that, you have…

717
01:03:42.440 --> 01:03:47.150
Rm 330: Pocket, and once you add thermal fluctuations, the backside of the pocket becomes completely

718
01:03:48.650 --> 01:03:54.340
Rm 330: So, the backside becomes incoherent. Would you actually still see the logic effects?

719
01:03:54.480 --> 01:04:02.869
Rm 330: Great question. I was hoping nobody would ask that. No, I'm just kidding. Very good question, but, you know, it is watching out, watching out the Yamaji effect.

720
01:04:03.020 --> 01:04:10.419
Rm 330: you know, have you thrown out the baby with the bathwater? You know, for this, obviously there's a Yamaji effect.

721
01:04:10.560 --> 01:04:23.509
Rm 330: But is there for this? Okay, we… that's not a calculation we've done. But what we have done, in this situation, we applied a magnetic field and looked for quantum oscillations of this pocket.

722
01:04:24.120 --> 01:04:31.289
Rm 330: So we can apply in the simulation much larger fields than you can in the experiments, and we clearly see that.

723
01:04:31.710 --> 01:04:34.539
Rm 330: That's… yeah, maybe I should have that picture.

724
01:04:34.890 --> 01:04:36.400
Rm 330: Yeah, so we've… that's…

725
01:04:36.980 --> 01:04:53.840
Rm 330: That was exactly the thing that we wanted to check. YMG would involve taking multiple layers, it's just too hard. Okay, thanks. But we did apply a magnetic field, and measure the free energy fluctuations, and see the oscillations.

726
01:04:55.480 --> 01:05:12.849
Rm 330: So, now, if I think of the cuprate phase diagram that you showed at the beginning, what about the phase transition at the boundaries as a function of hole doping, where you go into the antifer magnet on the side of the strange metal on the other side? What's the nature of those phase transitions, then?

727
01:05:14.840 --> 01:05:15.740
Rm 330: Alright.

728
01:05:21.430 --> 01:05:22.950
Rm 330: Yeah.

729
01:05:23.530 --> 01:05:29.989
Rm 330: Right, so which one? The one on the left and the one on the right. Yeah, so if this is FL star.

730
01:05:30.200 --> 01:05:34.100
Rm 330: then, this is… yeah, okay.

731
01:05:34.880 --> 01:05:37.960
Rm 330: When you have Fermi pockets, it becomes a bit complicated, but…

732
01:05:39.610 --> 01:05:43.499
Rm 330: This is described by condensing a sugar boson.

733
01:05:43.960 --> 01:05:47.739
Rm 330: This is described by condensing the charge on.

734
01:05:47.920 --> 01:05:48.680
Rm 330: Thanks.

735
01:05:49.650 --> 01:05:51.860
Rm 330: I mean, here, there's a very interesting…

736
01:05:52.110 --> 01:06:02.259
Rm 330: phase transition at zero temperature. Well, I could also imagine it could be just first-order phase transitions where this… Well, at finite temperature, Landau theory will give you the right answer.

737
01:06:02.750 --> 01:06:09.059
Rm 330: But if you want to… I mean, even here, for example, you know, this transition

738
01:06:09.580 --> 01:06:13.900
Rm 330: It's just costless dollars everywhere. That's in the sense of universal.

739
01:06:14.750 --> 01:06:17.210
Rm 330: But, if you look at the vortices.

740
01:06:17.360 --> 01:06:21.800
Rm 330: and the core of the vortex. Over here, you see the Wang-McDonald peak.

741
01:06:22.060 --> 01:06:25.920
Rm 330: Which is what BCS theory will give you. For you, here you don't.

742
01:06:26.130 --> 01:06:27.699
Rm 330: So on the scale of…

743
01:06:27.990 --> 01:06:36.610
Rm 330: you know, on the vortex score size, a bit larger, the behavior is quite different. But once you talk about many, many vortices, how do they behave? Nothing new to say.

744
01:06:36.870 --> 01:06:43.339
Rm 330: But on the scale of a vortex, on the scale of what's important for the electronic structure, what's important for emission.

745
01:06:43.800 --> 01:06:50.060
Rm 330: The transition here… And the transition here are very, very different. Here, it's a PCS transition.

746
01:06:50.230 --> 01:07:04.929
Rm 330: Here, it's a confined… I was probably thinking of the transition from the FL star phase to the right or to the left. Yeah, so the right is what I'll talk about tomorrow. That's where you get the strange metal, and that has to do with this other piece field.

747
01:07:05.130 --> 01:07:06.609
Rm 330: At least in this model.

748
01:07:06.890 --> 01:07:08.770
Rm 330: Going to zero.

749
01:07:09.950 --> 01:07:13.999
Rm 330: So, is there a phase transition within the supraculate state? No.

750
01:07:14.210 --> 01:07:16.780
Rm 330: That was a very important constraint on the theory.

751
01:07:17.040 --> 01:07:20.700
Rm 330: That there's nothing hap… so that's, yeah, that's a good point.

752
01:07:21.290 --> 01:07:22.679
Rm 330: What's different

753
01:07:22.850 --> 01:07:30.790
Rm 330: the nature, the qualitative nature of the onset of pseudosonic is completely different here and here. Here it's… PCS?

754
01:07:31.290 --> 01:07:33.009
Rm 330: Here is confinement.

755
01:07:33.490 --> 01:07:40.369
Rm 330: In the middle is probably quantum critical superproductivity, that's the most interesting in the highest temperature regime we understand the least.

756
01:07:40.730 --> 01:07:41.600
Rm 330: Oh.

757
01:07:41.740 --> 01:07:42.620
Rm 330: But…

758
01:07:43.120 --> 01:07:52.220
Rm 330: Although there is a phase transition between FL star and FL, if FL star and FL survive to zero temperature, there is a sharp phase transition between them.

759
01:07:53.000 --> 01:07:58.749
Rm 330: But the important constraint on all of this was that once they go superconnecting, there is no change.

760
01:07:58.880 --> 01:08:02.219
Rm 330: There is no phase solution in the superconductor phase, because

761
01:08:02.400 --> 01:08:06.359
Rm 330: both FL Star and FL, in their own way, in different ways.

762
01:08:06.670 --> 01:08:10.210
Rm 330: Are unstable to the same state, at least qualitative.

763
01:08:11.360 --> 01:08:12.270
Rm 330: That's…

764
01:08:12.940 --> 01:08:19.570
Rm 330: But, you know, for a while, I have hoped that it wasn't the case, but I… I see no experimental evidence for that.

765
01:08:19.750 --> 01:08:23.440
Rm 330: And that was a good day, because then I said, well, let's make it work.

766
01:08:23.550 --> 01:08:27.779
Rm 330: And this theory is the unique one that makes it work, really.

767
01:08:28.870 --> 01:08:29.990
Rm 330: Okay.

768
01:08:30.229 --> 01:08:33.580
Rm 330: If you don't know more questions, let's, thanks, Julie, one second.

769
01:08:45.370 --> 01:08:47.450
Rm 330: I don't pretending my soul.

770
01:08:48.510 --> 01:09:03.850
Rm 330: They have not been measured, most of them are multi-layers, so how are you… how are you gonna measure? Well, for what happened to an LSCO…

771
01:09:03.880 --> 01:09:14.830
Rm 330: It's in the manuscript.

772
01:09:15.250 --> 01:09:24.690
Rm 330: So in our paper, we've also computers.

773
01:09:24.899 --> 01:09:34.250
Rm 330: But it's not as simple as it is. You'll get a simple zero.

774
01:09:36.310 --> 01:09:40.470
Rm 330: Maybe, like, yeah, 60. Nope, nope.

775
01:09:44.029 --> 01:10:00.449
Rm 330: Wonderful talk. Thank you. Very clear. Even though I was very sleepy, I still understood. Yeah, it's amazing what one can do with all these games. I know. 20 years. But yes, you have to really think about it the right way. Right.

776
01:10:00.980 --> 01:10:13.190
Rm 330: So, like, explain the whole picture. I also, yes, and the lattice makes it so much richer than the appeal. Yeah, yeah, it is. A lot of it is lattice.

777
01:10:15.860 --> 01:10:40.619
Rm 330: Okay. I have to go prepare my lecture, so I will see what I have to do. Okay, we're going to the Chinese restaurant? Yeah, that's it. Okay. Yeah, that part of it, yeah, that part of it. Actually, I realized I didn't even use it. Yeah, you didn't… But this means that for tonight, I need to charge it up somehow. Can I just give it to you? Oh, yeah, absolutely. And then, pick it up.

778
01:10:42.600 --> 01:10:53.829
Rm 330: I'm going to be mostly there, except I teach, but, you know, I get jet stream. Like, dinner time, okay, unless somebody… I need to show some… I could use some other computer to show.

779
01:10:53.840 --> 01:11:05.929
Rm 330: Yeah, I detected Warhol and Heimer's. Yes, so, I mean, does it mean you have a separation of… That's the assumption, I mean…

780
01:11:05.950 --> 01:11:10.080
Rm 330: Otherwise, you have a sign problem. So we just… we take all the bosons.

781
01:11:10.440 --> 01:11:24.060
Rm 330: And do time-independent Hamil Monte Carlo. Oh, for each boson snapshot, we fully targeted. That is indeed that. The variants are much faster. Yes, yeah. And then…

782
01:11:24.840 --> 01:11:32.439
Rm 330: I mean, it's the bosons that are involved in all the phase transitions, so these bosons have a mass.

783
01:11:32.970 --> 01:11:34.340
Rm 330: And they're…

784
01:11:34.500 --> 01:11:45.490
Rm 330: Well, yes, they do, but they have a more complicated… you have to put them on a lattice, and the boson, they're moving by flux, that's also very important. They're coupled to a gauge field.

785
01:11:45.780 --> 01:11:57.319
Rm 330: So, if you take the low energy limit, the bosons have quadratic dispersion, but there's too many, not just one, in momentum space, just because of the flux.

786
01:11:57.910 --> 01:12:00.700
Rm 330: But what justifies?

787
01:12:01.280 --> 01:12:14.179
Rm 330: Well, nothing really, if you really want to do the full thing, you have a sign problem, so the best we could do. But also, you could, you know, you could say that… Yeah, yeah.

788
01:12:14.510 --> 01:12:35.230
Rm 330: All the phase transitions are associated with the boson, so at least near TC, just like in… Okay, we, static boson. Yes. Okay, okay, okay.

789
01:12:35.230 --> 01:12:49.129
Rm 330: But now… If you start thinking about the knife, Okay, okay. So, the…

790
01:12:51.310 --> 01:12:55.350
Rm 330: It's in any case in the East Wing. In that sense, it's…

791
01:12:55.860 --> 01:12:58.920
Rm 330: It's kind of an elliptical motion.

792
01:13:00.040 --> 01:13:01.429
Rm 330: It's not circular.

793
01:13:02.910 --> 01:13:08.689
Rm 330: you know, axial carries a little moment. That's… That's what the name is.

794
01:13:12.150 --> 01:13:15.090
Rm 330: This mixed stump will have Angular comment.

795
01:13:15.580 --> 01:13:17.429
Rm 330: It's not only the linear.

796
01:13:25.870 --> 01:13:28.520
Rm 330: Yeah, no, no, check.

797
01:13:28.710 --> 01:13:44.680
Rm 330: Yeah, so you… well, Indra is the name of the Hindo-European.