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Rm 330: In collaboration.

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Rm 330: Andrew Huxley at the University of Edinburgh, where I'm a Mariki fellow now funded by the European Commission, and I also have a Carnegie

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Rm 330: grant to study non-fermi liquid models, so I hope this talk won't be very boring to you, because I'm going to talk about single impurities with

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Rm 330: constant density of states, and I also plan to give an introduction into NRG, which, and perhaps he's an experimentalist, right? Yeah, he's an experimentalist. Wow, okay.

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Rm 330: So he, he works on, uranium-based heavy fermion compounds.

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Rm 330: And, and also unconventional superconductivity in uranium 2. So, here is the outline of my talk. I will, motivate, or I will…

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Rm 330: While we are studying non-fermi-liquid quantum impurity models, of course, it is to, understand non-fermi-liquid behavior that, has been,

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Rm 330: observed in many matters, but still the microscopic description is usually lacking. I will introduce the control program, which probably doesn't need any introduction to you, and then I move on to the

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Rm 330: To the result section, and show you how to be a non-fermic liquid quantum curating models that are protected by crystal symmetries.

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Rm 330: And in particular, I will discuss three models. The first one is the Coxis 2-channel condo model. I… I will show that,

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Rm 330: the construction, that, Cox, devised.

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Rm 330: Doesn't, conserve time-versal symmetry, so that might be a,

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Rm 330: indication why it has been so hard to, experimentally find a system that, fits this condo description.

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Rm 330: Then, talk about the topological condom model, which is another,

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Rm 330: non-fermi liquid model that is, that enjoys symmetry protection in cubic symmetry.

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Rm 330: And, the…

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Rm 330: main reason I'm giving this talk is that I would like to popularize this third model, which is the spin half impurity, J equals 3 half conduction electron condom over here.

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Rm 330: Viktor…

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Rm 330: which is also cubic symmetry protected and, and, and doesn't have the problem, that, Cox's construction has, and also…

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Rm 330: It's easier to, realize in, it seems to be.

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Rm 330: More, realizable in real materials, like, systems.

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Rm 330: And at the end, I will also briefly mention… so these models are all for impurities that have a doublet ground state, and at the end, I will talk about some non-Fermil liquid models that, that are… that describe impurities with a triplet ground state, also in a cubic field.

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Rm 330: Okay, so… Here are some… Some of the most studied and cleanest examples of non-family queued behavior in matters.

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Rm 330: So, there is the triumphantanum, copper oxide, where the,

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Rm 330: You see the registry that is linear.

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Rm 330: For different dopings near and at the, critical doping.

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Rm 330: or optimal doping, then, there is manganese, silicide, which shows a T to the 3 halves, resistivity.

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Rm 330: Over a wide range of temperature.

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Rm 330: And then we had a paper with copy a long time ago on the…

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Rm 330: thorium, rutanium to silicon to those with uranium, which has, this nice, non… which shows this nice non-ferring liquid behavior, namely a logarithmic, temperature dependence for the impurities susceptibility.

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Rm 330: Okay, sleep, yes.

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Rm 330: And then, okay, I'm not sure why this, I, I…

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Rm 330: I don't know how to get rid of that, for sure. Look at the minus. You see a minus in the script?

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Rm 330: That's it.

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Rm 330: Okay, so seemingly… okay, so the motivation is how to, how to,

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Rm 330: describe these properties with a microscopic theory. The seemingly unreactive problem is the Ocondo problem, as you all know, which was,

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Rm 330: observed.

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Rm 330: So a logarithmic temperature dependence of the electrical resistivity was observed in supposedly green samples in the 1930s.

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Rm 330: And then it took 30 years to find the theory to be able to describe this logarithmic temperature dependence.

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Rm 330: And then, but,

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Rm 330: So the condom, which was, so of virtue, but in the end was… condo was able to, get a lower rhythmic upturn the resistivity.

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Rm 330: For different, concentrations of the impurity concentrations, but this perturbative treatment breaks down at a certain energy scale called condo temperature.

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Rm 330: So, the first solution of the chondro problem

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Rm 330: came from Bierson, who devised the numerical RG method. He was studying the strong coupling limit of, these asymptotically free theories, like, so the quantum chromodynamics and,

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Rm 330: condo problem, and, published these two, Seminar foundational papers, the 70s.

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Rm 330: And, was able to. So, in the 70s, it was a question whether a QCD, can account. So, since they haven't seen 3 quarks.

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Rm 330: And they were not sure whether QCD is the right theory for the strong interactions, and Wieson managed to show part confinement by putting the theory on the Euclidean spacetime lattice.

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Rm 330: And, solving it, Monte Carlo simulations.

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Rm 330: And he also solved the condo problem with a different method of numerical RG, and then got an overall price for…

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Rm 330: Boy.

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Rm 330: about to start heckling. There are a few people before Wilson.

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Rm 330: Notably, Anderson of Nubach, and Hammond, who used to be here at Rutgers.

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Rm 330: who did the RG treatment of it long before Wilson. Of course, they didn't do the exact straw coupling, but they did come to the conclusion it was a ferminiquid before we did. Yes, you're right. Okay, so I think we shouldn't just drop Wilson. Yeah, so…

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Rm 330: So when, when was it? When… when did they publish the… I thought before?

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Rm 330: Yeah, the early 70s. Early 70s. 71, 72, 73. Thank you, Pierre.

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Rm 330: Okay, so I, I'm…

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Rm 330: Okay, I guess keep the RT interaction and RT interaction, if you… if you prefer, and move to the… but I can also…

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Rm 330: talk about it as you prefer. Give us your take on it. It's good to have your take on it. Okay, so to make a quantum impurity model amenable to this NRG treatment.

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Rm 330: First, you map the model into one dimension in energy space, and then you choose a lower, this longer discretization parameter, so a number greater than 1.

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Rm 330: and divide the conduction belt into logarithmically smaller and smaller intervals around the Fermi level.

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Rm 330: Then, to replace the continuum of electron states in each interval, you do a Fourier transform, and give only those electron states that are close to the equation, not in the position space.

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Rm 330: And to the level in Fermi monitoring momentum space.

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Rm 330: and making a unitary transformation. This way, you can map your… the conduction electron kinetic energy onto a nearest neighbor hopping form with exponentially decreasing… hopping amplitude along the so-called Wilson chain.

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Rm 330: So, the real zone chain is depicted in this figure, where there is a possibility to have multiple, multiple views on chains corresponding to different channels that I will capture, and here the impurity only couples to the

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Rm 330: Only couplers to the zero side of each chain in this treatment.

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Rm 330: Okay, so then you have a series of Hamiltonians defined along this chain, and by solving this Hamiltonian

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Rm 330: You, you can resolve the system properties at, lower and lower energy scales.

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Rm 330: So here is the solution of the one-channel condo with the larger iterations that…

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Rm 330: correspond to the low temperature, so zero temperature limit. And in 198 published a paper where they generalized the one-channel problem to

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Rm 330: a multi-channel problem.

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Rm 330: Which they showed as… so this corresponds to a firmly clean solution at zero temperature, and they argue that, in case of multiple channels are screening a screen half in 30, you can get a non-fermally clean behavior.

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Rm 330: Okay, so the most studied, example of multi-channel condo is a two-channel condo.

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Rm 330: model, which you already know, that has, this, Characteristic level spacing, it is such a danger.

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Rm 330: So… At zero temperature, which is a hallmark of non-thermin liquidity, and it has, logarithmically diverging,

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Rm 330: Specific heat coefficient, impurity susceptibility, and the square root, like, temperature dependence for the resistivity.

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Rm 330: So these are the impurity contributions. Okay, so now let's come to the results section. So…

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Rm 330: In 1987, Cox proposed that, by building, a Hamiltonian out of a non-grammer tablet, ground state.

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Rm 330: Surrounded by gummoids, conduction, etc.

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Rm 330: you can… this… this… this corresponds, effective to general condo description,

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Rm 330: At no temperatures, he caused the quadrupolar condo effect due to the

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Rm 330: due to the structure of the F2 impurity, ground state.

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Rm 330: And his motivation was to describe uranium-based cubic hair perifermion systems. And since then, many attempts

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Rm 330: We're made to, to experimentally, find a system which shows

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Rm 330: the hallmarks of, two-channel condo behavior. And to date, the most convincing experimental realization is from 2018.

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Rm 330: Where in, Presidium dot yttrium, iridium thing, iridium thing20, they claim to have found a behavior that matches the two-channel code, yes? What is the Miltonian video? I will show it in the next…

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Rm 330: Do they see a residual entropy?

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Rm 330: In this experiment? I think they, they tried to integrate, so, yes, I can… I'm not completely sure.

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Rm 330: So what, but it does look as if…

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Rm 330: non-feriminatory behavior is only in the limit of extreme low density. Is that right?

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Rm 330: Yeah, so, so this is the… The red and the curves are very low density, and it almost looks as if

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Rm 330: The 0.44 has a finite C over T at no temperatures, as if it's no longer a non-ferromatic width.

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Rm 330: Yes, yeah.44 is… Yeah, so that's what they published.

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Rm 330: It's not for a huge temperature range, either.

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Rm 330: And, what, that's the best I could find in the literature.

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Rm 330: Always .042.

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Rm 330: The, the, the, the, the shiny suit.

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Rm 330: Sorry.

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Rm 330: So, I'm really sure you didn't have me, Antonia in a second. So, I…

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Rm 330: But first, I show you the construction, how it goes.

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Rm 330: to build a non-ferrally liquid exchange Hamiltonian, you need an impurity ground state that is degenerate, and then you need conduction electrons that are… that have a degeneracy that is higher than the inferiority ground state. So, the only…

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Rm 330: Point group that makes this possible is the cubic or the octahedral point group, which has

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Rm 330: 3- and 4-dimensional irreducible representations.

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Rm 330: All the other… have, they, they don't, they don't have 4-dimensional, or, three-dimensional era.

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Rm 330: So, Cox argued that,

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Rm 330: that the tetragonal, hexagonal systems would also host this two-channel condo physics, but we found with Gobi

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Rm 330: A long time ago, that, those, systems would require fine-tuning to reach that, to reach that fixed point.

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Rm 330: But tetragonol has it, right? You said cubic, but tetragonol still has a…

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Rm 330: non-crammers doublet. It does have a non-crammers doublet. The problem is that it doesn't have higher dimensional, earwax, so… so, in… in tetragonal, they try to couple

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Rm 330: The impurity into two doublets of connection electrons, but since they are not guaranteed to be deterrent by the cubic field.

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Rm 330: That means that there is a crystal fits fitting which is relevant, and it will… so, unless there is some accidental degeneracy, or the… or the energy scales.

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Rm 330: play out in a certain way, you can't guarantee that, so it's not protected by… by cubic symmetry, because those, those terms, those crystal field splitting terms are there from the beginning, they are relevant. Sorry to push you on this a little bit, but, but…

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Rm 330: The two-dimensional representation

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Rm 330: of the non-chromos doublet is guaranteed in a tractor environment. That's good. And… and when you add an electron, or you remove an electron, you necessarily create a chromos doublet.

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Rm 330: That's also… And that's projected by time reversal symmetry, right? And so that's all you need for

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Rm 330: two-channel condo physics in this situation. So I think for a two-channel condo, you need

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Rm 330: 4 species of conduction electrons that are degenerate.

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Rm 330: and in tetragonal symmetry, you can only have doubly degenerate conduction electrons. Of course, you can… they can… you can couple more of them to the impurity, but, but there's… I think what you're saying is that the hybridization

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Rm 330: Of the two… the two degenerative orbitals would not be the same.

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Rm 330: And therefore, you'd have an asymmetric. Yeah, exactly. Yes, exactly. Okay, very good. So that, and that, irrelevant perturbation, then you cannot exclude it, so once it's there.

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Rm 330: it's irrelevant for two days. When you talk about AzRC, you mean beyond the time reversal, right? You're not counting the time reversal

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Rm 330: degeneracy has degeneracy. So when you say two-fold degenerate or four-fold degenerate, you include the…

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Rm 330: time reversal or not? So, so there are different… Temminology only. Yeah.

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Rm 330: So, there are different time reserve properties associated with the different erafs, so I think they are in this cluster table of… Yeah, yeah, no, no, I just want to understand the terminology. When you say that something is

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Rm 330: 4 for degenerate, or two full degenerate. You're including also the… It's everything. It's everything, yes. Thank you, yeah.

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Rm 330: Okay, so, so the, the only, the way, way to,

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Rm 330: to not have those terms that, here's mentioned is to have a cubic system.

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Rm 330: And then, if we have a doublet impurity ground state, then we can either couple it to a triplet of conduction electrons, or to a quartet of conduction electrons to have a… to have this frustration, to have something non-fermi-liquid.

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Rm 330: And it turns out that the simplest case where you have a non-crammers doublet, and you couple it to triplet conduction electrons against your permanent grid, then there is a…

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Rm 330: boxes construction, which is the non-crammer tablet ground state to dominate production records, which are… So, when you're talking about the concept of a bare impurity, or after screening?

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Rm 330: So, temporary impurity at the very infuri. High temperature, yeah. Before the interaction. Before the interaction.

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Rm 330: And when you talk about the symmetry of the conduction electron, you mean the symmetry of a localized electron at the first side of the symmetry of the localized electron. Yes.

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Rm 330: So…

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Rm 330: So this… this case corresponds to toxic setup. I will show you the Hamiltonian cross-section in a second. And there are two more cases.

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Rm 330: One is when you have a crammerstellarms state, and you couple it to a triplet of conduction electrons, and the fourth case is when you couple it to the export it.

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Rm 330: Okay, so just to check what I said was correct, so here are the erupts of the octahedral groups. These are the W representations.

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Rm 330: And, so, here you can see that, you can see the dimensions of each ERS.

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Rm 330: So… So there are no other possibilities. So the first case is a Coxis setup.

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Rm 330: he said that, so he assumed that he has an F2 electron configuration, and with a non-parameters double at ground state.

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Rm 330: So, with the L equals 3 conduction electrons and J equals 4 molecules, so the two states can be written… can be chosen to be these two states.

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Rm 330: And then he assumed that these two states hybridize with L equals 3, J equals 5 half conduction electrons.

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Rm 330: And more precisely, the part of those conduction electrons that transforms as a Gambonate quartet.

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Rm 330: You can express, these conduction electrodes with the…

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Rm 330: Jacqueline five, components of, of this,

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Rm 330: degenerate quantity left. And, in cubic symmetry, it will break into this gammaid doublet plus… plus a doublet.

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Rm 330: And the only way to have a cubic invariant exchange interaction is to… to combine the prime cap states on the impurity vector space.

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Rm 330: Boom.

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Rm 330: So this gamma was 3 times gamma was 3, which will, in cubic symmetry, break into these three, three ears. And then.

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Rm 330: You… when you… you build direct exchange interaction, and you construct the electron hold, creation times annually relation operators, the combined times convent part will…

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Rm 330: be… in cubic symmetry, we will break into, a couple of… a number of e-wraps.

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Rm 330: And then to have a Hamiltonian, you would need to take the scalar product of the same ERAP.

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Rm 330: Which means that…

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Rm 330: In this case, in Cox's case, you can have three terms in your Hamiltonian with independent Kathleen constants. Just to make sure I understand the symmetry, so the impurity transforms according to gamma3. Yes. And then the conduct… the piece of the conduction electrons I will keep is the gamma-8. Yes.

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Rm 330: And now you need to combine gamma3 and gamma8 into a singlet. Exactly. So, why do you just multiply gamma 3, gamma3, or gamma 8, gamma 8? How would I multiply… No, this is a bilinear in those states. Yes. And a bilinear of the conduction. What would be connected to conduction? And then you combine gamma 1 and gamma 1, gamma 2, gamma 2, gamma3, and gamma 3. Right, right, right. Okay. So we have, like, 3 possible interactions. Right, so these are, like.

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Rm 330: a single electronic exchange. The point is that we have 300 abandoned chains. Yeah, exactly. Okay. What is the exchange?

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Rm 330: So, these three J's…

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Rm 330: So, the first one is the gamma 1 times gamma 1, it's just a potential scattering, it's not interesting. It gives you a marginal perturbation, and then you have two others, so you have the gamma 3 times gamma3 contribution to the Hamiltonian, and the gamma 2 times gamma 2.

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Rm 330: And after… so, you made this correspondence

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Rm 330: or the spin… impurity spin operator, you can, define the S plus as this, outer product of your, of your, of your impurity state.

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Rm 330: And, you can define the… the different,

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Rm 330: Conduction electron operators as these bilinears.

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Rm 330: And then, if you make this correspondence, your Hamiltonian will assume, spatially an isotropic form.

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Rm 330: And, this is just an effective spatial anisotropy, so it's not, not in, real space.

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Rm 330: But, you see that

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Rm 330: as long as the coupling take, gamma 3 times gamma3 is greater than… than… than this.

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Rm 330: this coupling, your system will flow to a two-channel condo fixed point greater or equal, but as soon as this coupling becomes larger than the resistor, you have this rising light system, and you will flow to a firm liquid.

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Rm 330: So, already from the construction, You'll see that it's not,

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Rm 330: It's not guaranteed that, at low temperatures, so if you don't know anything about these couplings, that you have a two-channel condo.

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Rm 330: fixed point. You have a third possibility, right? Because you have three reps. Yeah. I have a potential board. It's sort of like the XY symmetric, except X and Y are X and Z are symmetric, Z different.

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Rm 330: Right? And that's attractive.

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Rm 330: So… so that's one reason… that could be one reason why it's not so easy to find a system that, is described by Foxy's Construction.

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Rm 330: A question about that, this is pure… the gamma 3 times gamma 3 is pure XY.

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Rm 330: You've got two-channel XY, right? It's Z and X, but it's sort of effectively

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Rm 330: two-channel XYP, right? And the XY condo problem doesn't care about whether it's Ferromagnetic or anti-ferromagnetic?

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Rm 330: So…

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Rm 330: you could, I suppose, have hunks, I don't know, some kind of ferromagnetic version of this that would also work.

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Rm 330: Maybe, yeah, yeah, what you read, too. It wouldn't come from super cheap, it would come from some other…

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Rm 330: Yeah, but, like, yeah, so you need to make sure that this Kathleen doesn't, override the…

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Rm 330: Yes. Rakuten. And Ising… Would normally be…

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Rm 330: Huizing is only unstable when it has J… But associated with it.

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Rm 330: don't… it doesn't flow on its own, is it?

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Rm 330: Ising doesn't… the beta function is zero for Isaac. Okay. And so, we wouldn't give you a Fermi, could you have a decouple of spins?

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Rm 330: Yeah, so, okay, then correct the coupled spins, but you don't… Yeah, so then it would do nothing, and and no matter what the size of the other coupling would be, it would still flow to strong coupling.

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Rm 330: Well, I think… So, I think that as soon as this seems Greater than this coupling.

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Rm 330: It's only Ising. If it were bigger and it were XY, I would agree with you, but it's only Ising.

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Rm 330: I didn't know, but…

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Rm 330: I guess to really be sure, you've got to do the scaling with both terms present.

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Rm 330: You see what happens, but icing on its own does nothing.

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Rm 330: I, I think it, it will, it will orient your, your spins, and you don't,

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Rm 330: You don't have this frustration.

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Rm 330: Because Ising… because Ising can't float a strong company.

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Rm 330: It's only the other terms that were grown.

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Rm 330: But when this one dominates, these terms are just the perturbation twice, so… Yeah, but a relevant… These are irrelevant perturbations, I think. Oh, that's what I would like to see. I can show you the… I can show you the… Yes, not obvious.

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Rm 330: About the analogy, certain sports.

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Rm 330: I, I showed it to… entourage, and she said that it's, oh, then it must be true.

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Rm 330: Okay, we can buy that. There is a range of Js, right, in which there is that provider. Sure, sure, I'm just curious about the general base aircraft. Right.

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Rm 330: Okay, so… By the way, this would be the territory.

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Rm 330: of, of Anderson or Belcomer.

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Rm 330: Basically, start with the JZs, do that exactly, but for a turbine in the J bar.

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Rm 330: I think it's irrelevant. I mean, according to analogy, it's irrelevant.

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Rm 330: Okay, so, so… It's relevant. Just to state my position. Okay.

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Rm 330: And what is your opinion based?

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Rm 330: Do you cover this?

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Rm 330: No, I think it would… it… I don't see… well, it would be… I think it would be rather like the Ising-Combo model.

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Rm 330: But where the corrections are J squared.

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Rm 330: And negative, so they always grow, but I don't know. I haven't done it, I must admit. I guess I'd like to know from Antoine, if he's the one who says it's perfect, why?

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Rm 330: The, the other terms aren't relevant.

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Rm 330: Are they irrelevant? Are they… presumably, they're only irrelevant if you actually calculate the beta function.

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Rm 330: Right? Because it won't be on the basis of…

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Rm 330: it won't be on the basis of basic naive skating, because you're in the critical dimension. So you actually have to calculate that second order.

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Rm 330: those beta function terms, right? Right. And I'd like to know what they look like. Isn't the Anderson of a common thing that the JZ would provide the phase shifts in those calculations, and the JFAR is sort of like the one that's making the boundaries, and that flows

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Rm 330: Yeah, but they always get… Yeah, yeah, yeah. I mean, for…

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Rm 330: Of course, if you have ferromagnetic JZ, and maybe that's what you're talking about, then it does scale to the Ising fixed point. Yes. But if you have anti-ferromagnetic JZ, it scales away, so it would be very useful

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Rm 330: to know what the scaling diagram looked like, that the Uba-Anderson-Hammond scaling diagram looked like to this problem? I will check the… I will check it in years, but you should remember that Anderson Ahuwal-Hammond

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Rm 330: computes perturbation theory around J small. Yes, and the relevant question for what she's talking about is whether at the critical point that she's interested.

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Rm 330: which is a different critical point, whether around that critical point, that perturbation will be relevant or irrelevant. Oh, I see. So that doesn't help you. Okay, that's a good answer. Thank you. I like that. Okay, thank you very much, Gabby.

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Rm 330: Okay, so let's see. If that is the right answer. No, that's the right answer, from an energy perspective. But that… I guess that would be the question. I think it's a very good point. She can answer that. Yes, what do you think? Do you think Gabby's argument is the right one?

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Rm 330: Is it weak coupling or strong coupling? You're interested in non-fermi liquids, right? So you want to sit around the non-fermi liquid fixed point and first orbit. Yes.

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Rm 330: Okay, but she can do that. But it scales the strong coupl… what you're saying is it still scales the strong coupling, but that strong coupling fixed point is a fair meeting.

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Rm 330: There is sort of a silly way of doing things. Actually, maybe not so silly way of doing things. Go to the critical part.

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Rm 330: Yes, I think as the Kandi was saying. Right, right, right, very right. Which critical… The two-channel critical part. Yes, yes. So, all symmetries exist. Yes. Right? Iconisotropy exist. I now ask, if I did a little bit of anisotropy around it.

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Rm 330: what do they look like? What are… what is that nice trophy going to be made of? It's going to be made of spin times the current interpreters.

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Rm 330: Now, Spin has been replaced by the modern. Yes.

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Rm 330: Okay? So it's a myron of Fermion times bilinear, so myron of fermions. So, this is the so-called leading relevant operator. So I don't fully understand why slight JZ perturbation would immediately flow somewhere away. It's not slight. If it's very large, maybe. It's not slight JC, so JZ is the dominant, so as soon as… Right, but my gut instinct would be…

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Rm 330: that it is the leading irrelevant operator that actually includes the Wilson ratio or something. Around the exactly isotrop. In other words, it would hybridize the Majoranas with the… Right, yeah, it is not 3 Myronutrons.

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Rm 330: That's female product. Okay, so at the end of the day, you suspect is irrelevant? I suspect slight anisotropy around the point is irrelevant in all directions.

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Rm 330: Okay. Right? But, okay, but since you are saying this, I should understand one time. But that's what I'm saying, that if there is a small isotropy, then you get the two-channel condo. Yeah, so two-channel condo, isotropic, two-channel condo, ordered by a small isotropy.

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Rm 330: I'm claiming that is 27th. Yeah, but this one is not so small now. This one is the… is the… Okay, okay, okay. I don't want to take over this, but we should solve this one. An interesting prophecy. Yeah.

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Rm 330: Okay, so… so I would like to argue that, there is also a problem with the time reverse asymmetry in this, in this construction.

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Rm 330: So… Cox constructed, Jacqueline half conduction electrons from L equals 3 and spin half in half.

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Rm 330: And, if you take the time-wise asymmetric properties, then

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Rm 330: So, theoretically, when you look at the impurity spin operator, which is made out of a non-crammers doublet, then it's a time versus symmetric even PRS-even operator. And then you couple it

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Rm 330: to the spin operator made of, gamma-8 conduction electrons, which is,

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Rm 330: which is… which is going to transform as a spin under Time Reversha. But actually, you have to,

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Rm 330: Going and looking to the details and… and see that,

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Rm 330: This, so the gamma… the gamma 3 times gamma3 term, we have break time reser 3.

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Rm 330: Whereas the gamma, 2 times gamma 2 thirds is odd under 10 reversal G. There's time reversal, too. Hamiltonian should be…

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Rm 330: should not change under time. Yeah, so that's a problem with this construction, but if you substitute in L equals 1, F equals 1 half, and J equals 3 half conjache electrons, which also furnish a gamma 8.

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Rm 330: era of the QB group, then

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Rm 330: You can show that, in that case, the construction works.

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Rm 330: I mean, it's time versus asymmetric. Did he… did he make a mistake with the…

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Rm 330: Did he therefore make some kind of mistake with the Schriefer-Wolf transformation? Because the underlying Anderson model would be time-reversely variant.

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Rm 330: And so, if you integrate out the charge fluctuations, you should get a time reversal invariant.

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Rm 330: Hamiltonian theme. The underside-Anderson model would be a kind of Olek-Andre model.

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Rm 330: Right? And that wouldn't break time reversal Seminar 3. I think he hasn't carried out the Schiffer of transformation. He only built the condo exchange term using the symmetry argument, so he acknowledges the…

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Rm 330: That means he made a mistake in the tree-for-warf transformation, because we know that the Ballik-Andre model exhibits two-channel physics.

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Rm 330: then if he can have the… the… the Schiff Awards, which I'm not sure, because I haven't seen the derivation in the papers, then he did make a mistake, but you can check that in the model for… for this…

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Rm 330: for the non-8, part of Joseph breaks times where symmetry, whereas if you go

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Rm 330: to the Jake was, seven and a half.

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Rm 330: and then you project out the gum-wide conduction equals, then you can also be it. So there is an alternating, depending on how you build your gumway aids, you either get…

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Rm 330: The breaking, or you get diversal symmetry.

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Rm 330: So…

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Rm 330: Okay, the second case is the topological bundle case, where you have a parameters of, like, the impurity ground state, and you couple it to gamma 4 or gamma5 conduction electrons.

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Rm 330: In that case, the construction goes the same way, so you've construct the bilinears from your

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Rm 330: On, on their impurity, ground vector space, and, and also the, these, So… Electron hold.

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Rm 330: from the conduction electrons, and you see that in that phase, you only have two possible independent couplings in the Hamiltonian. The first one is, again, a potential scattering.

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Rm 330: Whereas the second one, we'll give you the so-called topological condo model, which is interesting in that it's a simpler model than the two-channel condo, because it has less degrees of freedom. It gives you a non-family bit ground state, but

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Rm 330: It's, not clear how to…

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Rm 330: Realize it in real materials, as, it's hard to get, liquid one collection electrons.

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Rm 330: Without, so you'd have to apply a magnetic field or something.

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Rm 330: To… to, why is it called topological?

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Rm 330: Let's go twice that, too.

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Rm 330: Because they, they, so, the term comes from 20… 2013, I guess, and they studied, they, tried to realize…

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Rm 330: The… the impurity using, one-dimensional,

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Rm 330: superconducting, so this kit I have changed with, my runoff fermions, but… so it's just, I,

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Rm 330: If it's a way of, they, they wanted to have some topological protection.

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Rm 330: of these non-ferment properties, but this model existed already in the 1990s and was studied by Fabrizio and Gogolin.

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Rm 330: And they show that, and also, Ahluwan showed that this is,

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Rm 330: This can be… so there's a correspondence between this model and the four-channel condo model.

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Rm 330: So, yeah.

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Rm 330: If that's a satisfactory answer.

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Rm 330: It's a new passion of living.

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Rm 330: Okay, anthropological.

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Rm 330: Okay, I calculated the thermodynamic… What I remember is that it had something to do with coupling an island, the superconducting island.

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Rm 330: to another superprotecting chain, and that he… he made the two channels robust. The… the microscopic physics

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Rm 330: was such that there were no relevant perturbations. That was the excitement around it. I see. That's the recent excitement, recent meaning in the last 10 years. Yeah, the recent excitement. I think that the guys in Cambridge did it, no? I mean, it was,

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Rm 330: your colleagues, peers,

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Rm 330: Berry and Cooper. Nigel Cooper, Cooper. Nigel Cooper. Niger Cooper, the other Steadman, Berry, Berryman, yeah.

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Rm 330: I see. And the important point, that was very interesting, because the microscopic physics killed the usually irrelevant operator, which made the

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Rm 330: two-channel condos, so hard to observe. I see. So they had a real thing that would be two-channel. So they made this using a higher chain? Not really, all you needed is some super… yeah, it had that flavor, but it had some superconducting elements, it had to be coupled in some way, but it was good.

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Rm 330: That's all.

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Rm 330: So, for this model, you have a zero-point entropy that's, half log 3, and, and,

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Rm 330: Susceptibility.

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Rm 330: And the specific heat coefficient scales as D to the minus 1 over 3.

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Rm 330: We calculated this since it,

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Rm 330: NRG, but NRG is not very useful for, for example, for the specific heat coefficient. It is, numerically very challenging to get a logarithmically divergent,

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Rm 330: specificity coefficient, so you couldn't, infer these, exponents from an algae, so it's from the fabricity of a body absorption that its exponents are known.

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Rm 330: And then, I think the third case, which is the most, interesting, is when you have a grammar sublet impurity, and you couple it to Bonsai conduction.

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Rm 330: And in that case.

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Rm 330: you will have… you do the same construction, and you will have three possible, three independent governings in your… for your exchange Hamiltonian terms.

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Rm 330: And it turns out that the first coupling is the spin-spin coupling, so the impurity spin times the spin 3 half,

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Rm 330: Of the con-action electrons.

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Rm 330: Which looks like this, and there is no dual non-fermalic winter.

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Rm 330: Fixed point, and then there is a second coupling.

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Rm 330: Which, which is, okay, so, so this, this has a non-fermi liquid fixed-point structure with, this exciting level spacing structure.

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Rm 330: And it was shown to be… so there is this correspondence between the 10-channel condo model and this model, which I can explain the level of spacing ratio. So.

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Rm 330: There's a… the… the main plane from… or maybe I'll…

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Rm 330: I mean, I'm wrong, but

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Rm 330: to me is that every spherical isymmetric exchange coupling that is a scalar product of two vector operators can be mapped onto an ordinary YT channel condo each spin height. Is there an easy way of understanding Y10?

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Rm 330: And then there's a formal, but that's…

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Rm 330: show is that… that… so, this is, like, 6 electrons, right? Yes. So, the 6 electrons, okay, acetylcharge 6. Charge checks away 1, and basically what happens is that there's a modern degree of freedom, and I think an acetyl level 3, or 5 was of freedom.

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Rm 330: Okay, there's this true level K that takes up the spin group, right? By looking at the… just the current, and it's, its, its algebra.

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Rm 330: That, that was what was in our paper. Yeah, yeah, yeah, so I, I should, I should have to look at my own paper, but you can say, okay, I have this, this…

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Rm 330: is being 3-half representation electrons, right? So I can make the currents, like psi dagger, 3 half generator psi, and you can ask, what is its current algebra?

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Rm 330: So the ground algebra, of course, if you do commutation, you'll just follow the algebra rules. But if you do the,

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Rm 330: the two-point function.

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Rm 330: That's, like, effectively how many channels you have.

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Rm 330: Okay, and you have to compute the, sort of, the generator, time generator, trace, square, etc. sum, right? And that becomes an SC2 level at different K.

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Rm 330: Okay. So, so it looks like, like, a higher number of sandals. I can believe it's higher number. Right, right, right. So exactly what number? I, I want… I want to say 3, but I think… I think it's N. No, it's not, it's N. I think it's N. You know better than me.

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Rm 330: Right, right. According to the formula in these two papers. Okay, fine. But the fact that you have certain current algebra… Right. …is just an algebraic statement that I follow from the math, it doesn't mean that there are…

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Rm 330: It's realized by simple electrons.

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Rm 330: No, it's not. It could very well be that it's not, and that it's a different composer, something that, as long as it obeys that algebra, is good. So the simulation in that paper was that, okay, how do I do the quanto perturbation theory? The quanto perturbation theory is spin dot

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Rm 330: A current. If the current correlator is exactly the same.

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Rm 330: has some SC2 level K. Yeah. Okay, for some K function of J, then it'll look like the perturbation theory is the same. Yeah. Okay? Now, so that's where the hope is, that it will be like

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Rm 330: As you to a certain number of channels.

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Rm 330: current algebra, okay? Now, it could be that there is a relevant operator somewhere that messes the one. That could be the case, okay? The more you'd see that in the database, the more you'd see that in the scaling… But you have to be careful, because what we are sort of saying is that take the scaling limit of everything.

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Rm 330: Right? There could be a way to get cut off, or something introduces some other operator and misses him up that you don't see. And can I ask about these two papers? What mechan…

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Rm 330: What… what's…

318
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Rm 330: scheme did they use? Was it bosonization? Was it conformal field theory? So the second, I believe, was conformal field theory. Yeah, it was just trying to identify what the algebra of the vectors are, and hoping that that works. The first one was bosonization and… Bosonization, okay.

319
00:47:46.760 --> 00:47:53.469
Rm 330: Yeah, I'm not sure. Vosalization of the… of the to-dose point to this model, I guess.

320
00:47:53.720 --> 00:48:01.610
Rm 330: But, yeah, I… Okay, and… so…

321
00:48:01.740 --> 00:48:06.270
Rm 330: Then there was the second coupling, Or in this

322
00:48:06.450 --> 00:48:20.699
Rm 330: And it turns out that… which is… which doesn't have full spherical asymmetry, and it turns out that it flows to the same fixed point as the tangential condo fixed point.

323
00:48:21.030 --> 00:48:25.490
Rm 330: And it has, this ugly expression for the…

324
00:48:25.890 --> 00:48:34.860
Rm 330: zero-point entropy, and the susceptibility goes as D to the minus, 3, 2 over 3.

325
00:48:34.980 --> 00:48:41.649
Rm 330: As well as the specific heat coefficient, whereas the resistivity… You were right, it was K time.

326
00:48:41.960 --> 00:48:54.369
Rm 330: that that works out, too. So the, the, the resistivity has this 1 over 6 scaling property, as t goes to 0.

327
00:48:55.000 --> 00:49:00.990
Rm 330: And, yeah, so, so, so, so this model, is,

328
00:49:01.220 --> 00:49:09.059
Rm 330: She's, has diversal symmetry, and, it doesn't, have,

329
00:49:09.280 --> 00:49:12.000
Rm 330: It doesn't have the problem of,

330
00:49:12.690 --> 00:49:24.510
Rm 330: of the coffee construction, that, you have a term that, if it dominates, it will spoil the non-fermal liquid behavior.

331
00:49:24.650 --> 00:49:32.520
Rm 330: And I think this, this has a greater chance of existing in, in,

332
00:49:33.760 --> 00:49:38.790
Rm 330: Real materials than the two-channel condo and the topological condo.

333
00:49:38.790 --> 00:49:46.699
Rm 330: Because… but I'm not sure, so all you need is a cubic system, an impurity leader, traverse of that ground state, and

334
00:49:46.700 --> 00:50:00.729
Rm 330: Sorry, I think I said something wrong to you. The numerology is that there are four permanents, so I did four central charts. Yes. Okay, in the construction, you can see… so this one goes for pure charts.

335
00:50:00.990 --> 00:50:06.919
Rm 330: The pure charge degree of freedom. So, one person is out. Okay, so I've left with three.

336
00:50:07.150 --> 00:50:21.280
Rm 330: Turns out that if you do this sort of personization way, you will see that there is a cosine of something, so there is a myron fermion hanging there. So, you have to explain two and a half. Yes. Central charge left, so two and a half degrees of freedom.

337
00:50:21.380 --> 00:50:35.630
Rm 330: Okay? And turns out, if you take 3K over K plus 2, which is the central charge of this into 11K, you said K over 10, you get 30 over 12. That's the arithmetic I was bringing in right now. Oh, I see. Okay, thank you. And if you work it out, it actually is the 5 over 2.

338
00:50:35.910 --> 00:50:49.530
Rm 330: That would provide this. So, it kind of works out in that particular case. Okay, that there's a breakup of these degrees of freedom as a charged Bonsai and AC to level 10, and a minority.

339
00:50:49.650 --> 00:50:53.140
Rm 330: That's what I've been doing. Thank you. And, and…

340
00:50:53.400 --> 00:50:59.300
Rm 330: Just a follow-up, what was your motivation behind studying this model? Was it… Okay, so he's already gonna be…

341
00:51:00.240 --> 00:51:10.049
Rm 330: younger kid, historically, ran into another king, okay, with Cox's lab, and say, oh, they're looking at this higher spin place.

342
00:51:10.220 --> 00:51:17.630
Rm 330: Okay? So he says, oh, they are doing this energy, and they have something… okay, you know about performance theory, what should it be?

343
00:51:17.740 --> 00:51:28.040
Rm 330: Okay, so I said, oh, but maybe take these higher-screen things, look at their current algebra, and try to make a guess about what effective channel they have.

344
00:51:28.200 --> 00:51:33.290
Rm 330: Right? And at least, I believe in the first two cases, it kind of works out, and then…

345
00:51:33.410 --> 00:51:38.040
Rm 330: Cox and Kim and others had some pushback that for a larger case of brokenness.

346
00:51:38.460 --> 00:51:50.359
Rm 330: Okay, with energy, but I… it has also sort of left a little bit in the dust, so, like, you know, nobody has seriously pursued to see why things are different, yeah.

347
00:51:51.340 --> 00:51:52.050
Rm 330: Okay.

348
00:51:52.390 --> 00:51:53.949
Rm 330: Okay, so… Thank you.

349
00:51:54.460 --> 00:51:57.079
Rm 330: So the last part is about the…

350
00:51:57.380 --> 00:52:01.109
Rm 330: The case when you have a triplet state.

351
00:52:01.480 --> 00:52:04.630
Rm 330: And in that case, there is only one.

352
00:52:04.880 --> 00:52:17.800
Rm 330: combination, so you have a tripatic purity, you can only couple reaction electrons to have a concentration, as it turns out that you have 6 possible couplings.

353
00:52:18.000 --> 00:52:26.630
Rm 330: One of them is, which is the dominant coupling, which is quadrupolar, quadrupolar, turq, and you will also have,

354
00:52:26.970 --> 00:52:34.550
Rm 330: So, altogether, 3… can flow to 3 different types of non-ferring liquid fixed points.

355
00:52:34.560 --> 00:52:52.440
Rm 330: But the quadrupolar, quadrupolar term is the dominant, and what's also interesting is that all of these are given impurity contribution to the specific heat and the magnetic susceptibility. So the specific coefficient of RT positive minus 2 over 3.

356
00:52:52.500 --> 00:52:59.800
Rm 330: And the question whether this… to Anira, whether this quadrupolar, quadrupolar coupling can also be…

357
00:52:59.880 --> 00:53:03.040
Rm 330: Understood the intent of it.

358
00:53:03.310 --> 00:53:07.690
Rm 330: But hiring, bought each other, condo models.

359
00:53:09.360 --> 00:53:10.760
Rm 330: So, okay.

360
00:53:11.340 --> 00:53:13.959
Rm 330: Here are my conclusions.

361
00:53:15.200 --> 00:53:27.379
Rm 330: So I showed you how to systematically derive all possible non-feri liquid interaction exchange couplings for doublet and triplet impurities.

362
00:53:27.900 --> 00:53:35.550
Rm 330: For cubic symmetry, I argue that one should be careful to check the time universal symmetry.

363
00:53:35.660 --> 00:53:38.209
Rm 330: for… for these Jamiltonians.

364
00:53:38.380 --> 00:53:39.439
Rm 330: And then…

365
00:53:39.930 --> 00:53:48.999
Rm 330: And I think what's the most interesting is that, this, relatively little study, spin half impuity, spin 3 half.

366
00:53:49.210 --> 00:53:59.629
Rm 330: Conduction electron water is, the most, seems most feasible to be realized in, real systems.

367
00:54:00.350 --> 00:54:05.150
Rm 330: M… The question is whether, okay, and,

368
00:54:06.260 --> 00:54:14.620
Rm 330: So, what the purpose of my visit is that I would like to

369
00:54:14.890 --> 00:54:31.800
Rm 330: understand what type of anions can be found at this fixed point. So, at the two-channel condo fixed point from the American construction, we know that there's a Bairana fermion, which is used in,

370
00:54:31.800 --> 00:54:39.959
Rm 330: So Microsoft claims that they built, Topological quantum computer,

371
00:54:41.100 --> 00:54:44.329
Rm 330: on the principle of creating Major Majorana fernials.

372
00:54:44.590 --> 00:54:57.409
Rm 330: And, but they are not ideal for quantum computations, as they don't furnish a universal grade set, and they only, generate a discrete number of,

373
00:54:57.510 --> 00:55:08.600
Rm 330: states instead of a continuum, and the question is whether in these models, where the… so, from all of the…

374
00:55:08.710 --> 00:55:26.690
Rm 330: non-fermic with quantum imperative models. The onion in the low temperature phase has already been identified in three cases for the two-channel condo. There's this Myurana fermion for the three-channel condo. They found the Fibonaccianion.

375
00:55:26.840 --> 00:55:33.039
Rm 330: And for the so-called double-charged condol, there is a so-called 3-3 paraffinion.

376
00:55:33.180 --> 00:55:36.590
Rm 330: And the question is that, for example, in the…

377
00:55:36.970 --> 00:55:40.620
Rm 330: The spin-half impurity date was 3 half.

378
00:55:40.750 --> 00:55:45.920
Rm 330: Conduction electron model, what kind of anion you find, and what are the

379
00:55:46.040 --> 00:55:53.190
Rm 330: the braiding rules and the… and the fusion algebra, whether it… it… it gives you a…

380
00:55:53.310 --> 00:55:59.190
Rm 330: a full set of gates, as opposed to the Majoranas.

381
00:55:59.340 --> 00:56:02.849
Rm 330: So, thank you very much for your attention.

382
00:56:10.090 --> 00:56:25.010
Rm 330: asked enough questions, or some more questions. Can I just ask about your spin a half, spin three halves? I wasn't quite sure about that. So that's not just a spin-a-half screen by a spin three halves, which would give an under-screen condo model. It's something different to that, right?

383
00:56:25.250 --> 00:56:29.619
Rm 330: Let's a spin half, spin wider, by…

384
00:56:30.870 --> 00:56:34.929
Rm 330: spins 3 half, or J plus 3 half conduction electrons.

385
00:56:36.290 --> 00:56:40.240
Rm 330: Oh, it's… it's spin three halves conduction. Yes.

386
00:56:42.520 --> 00:56:44.100
Rm 330: Thank you. Thank you.

387
00:56:45.470 --> 00:56:53.390
Rm 330: Since you're, working with an experimentalist also, I thought I would ask the following question,

388
00:56:53.580 --> 00:57:06.369
Rm 330: that relates to Pierce's exchange with you about the chitragonal crystal. So, if I… if you have a non… you told us about an experimental system where we had a non-commerce doublet in a cubic environment.

389
00:57:06.840 --> 00:57:17.990
Rm 330: And it seems to have features that are very similar to the two-channel condo model. But now, if you apply strain and turn it into a tetragonal system, within

390
00:57:18.280 --> 00:57:26.829
Rm 330: it go from an isotropic, two-channel condo to an anisotropic two-channel condo? Would you see the…

391
00:57:28.090 --> 00:57:32.800
Rm 330: It would, it would drive your system to a firm migraine plus your…

392
00:57:32.840 --> 00:57:51.969
Rm 330: would introduce this symmetry breaking between the… so it wouldn't have… You'd break the non-chromost anymore. You'd break the gamma-8 at the… Oh, you'd break the gamma 8, it wouldn't have… so there would be no way of keeping… I wanted to know if you could go from

393
00:57:52.440 --> 00:57:57.880
Rm 330: Isotropic from the two types of, two-channel condoms.

394
00:57:58.710 --> 00:58:00.420
Rm 330: But I guess not. Okay.

395
00:58:00.680 --> 00:58:16.839
Rm 330: In a follow-up to Bramy's question, you mentioned at the beginning your work on uranium dilute… dilute uranium in thorium with helium-2 silicon here, which of course is dragon. So how come there's not very liquid behavior there?

396
00:58:17.210 --> 00:58:28.899
Rm 330: Yeah, no, that was sort of where… yeah, it was in, in a… in a window, in a temp… in a small temperature range, I guess, so if you would go to lower temperatures…

397
00:58:29.110 --> 00:58:42.890
Rm 330: then… so I guess it depends on the… the value of the condo temperature, and that… I guess it means that somehow the condo coupling in the two channels is, by chance, equal.

398
00:58:43.650 --> 00:58:55.460
Rm 330: Yeah. Is that what you're saying? Right, right, they are equal by construction… well, no… so the… I think what the construction went that the time reversal symmetry,

399
00:58:55.490 --> 00:59:13.159
Rm 330: implied that the couplings are equal, but you could have this other term that… I think we pointed that out. Yeah. We think we pointed that out, that there was some, potentially relevant perturbation in there. Yeah, so that… It's a fine print.

400
00:59:13.780 --> 00:59:32.719
Rm 330: But it wasn't… but I… I got the impression that… that if you were to translate this to the bollock-Antrey model, then of course the conduction electrons have spin and orbital indices associated with them, and so they are the… they are the representation that doesn't exist in

401
00:59:32.850 --> 00:59:42.910
Rm 330: in… in, tetrical environments, but would exist in a cubic environment. But is… is it then that the hybridization

402
00:59:43.070 --> 00:59:45.579
Rm 330: With the two channels would not be equal.

403
00:59:45.930 --> 00:59:52.269
Rm 330: So, I think the hybridization would be equal, probably, because somehow

404
00:59:52.470 --> 01:00:00.750
Rm 330: time versus symmetry connects the two channels, but you… That would connect up and down, but it wouldn't connect one orbital with the other orbital?

405
01:00:01.620 --> 01:00:14.360
Rm 330: But in our construction, in our construction for the case, if I remember correctly, one channel corresponding to the 5 half

406
01:00:14.540 --> 01:00:18.399
Rm 330: Minus 3 half, and the other was…

407
01:00:18.400 --> 01:00:34.840
Rm 330: the 3 half minus 5 half, or something like that, so… so 10 versus symmetry did connect the two chatters, but you could have had the extra, splitting between the, the, the two, the two… these two,

408
01:00:34.840 --> 01:00:50.150
Rm 330: the entity of states might be different. Is that it… between the two different channels? So you have, you have, you have, from the start, symmetry allows you to have, crystal fields fitting between the two grammar stufflets, or… yeah, so… so,

409
01:00:51.780 --> 01:00:55.760
Rm 330: Oh, you can jump back, but I don't mind. Okay.

410
01:00:55.890 --> 01:00:59.010
Rm 330: Okay, so, any questions?

411
01:00:59.230 --> 01:01:20.039
Rm 330: Actually, it's very general. I mean, it seems to me that now it's probably time. I mean, have you thought of just putting some DMRT cell consistency there? The reason why I'm asking is because what struck me about this problem always is that people are studying the alloy, okay? They're wearing X, and then they're claiming, oh, I see this, I see that.

412
01:01:20.040 --> 01:01:26.719
Rm 330: So just to know what people are talking about, one should really study the disorder system and see what X

413
01:01:26.720 --> 01:01:37.150
Rm 330: is the single impurity, what X is lattice, and all that can easily be done now. You have all the machinery, all you need to do is learn how to do the disorder average.

414
01:01:37.200 --> 01:01:40.039
Rm 330: And then, how to put the self-consistency.

415
01:01:40.140 --> 01:01:54.849
Rm 330: Yeah, that would be interesting. I think Fabian Kubler has the machinery. He has studied something else. He has not studied that problem. He has not studied… okay. Because the spin fluctuation is so slow like this, this is sort of…

416
01:01:56.050 --> 01:02:03.999
Rm 330: That 1 over T9 correlated, right? If you have these states ever interact with each other.

417
01:02:04.200 --> 01:02:14.160
Rm 330: the chance of them ordering is very high. Of course. Right? So, even if there was something that protected, magnetic order must probably take over.

418
01:02:14.160 --> 01:02:33.039
Rm 330: But then the question is, how dilute… Yeah, high dilute. What temperature? Right, right, right. So that is all the material C questions. Beyond just saying relevant… Exactly, instead of just talking, we're gonna do is look at an experiment and say, this temperature range, I expect this, is that…

419
01:02:33.040 --> 01:02:35.870
Rm 330: It's interesting, because at the concentrations you quoted.

420
01:02:36.150 --> 01:02:41.489
Rm 330: If you'd done that with iron and copper, you'd be right into a spin class. Right.

421
01:02:41.800 --> 01:02:46.269
Rm 330: Absolutely. So… so here you're not, somehow. That's interesting.

422
01:02:46.910 --> 01:02:48.190
Rm 330: Here we go.

423
01:02:49.270 --> 01:02:51.080
Rm 330: also really complicated.

424
01:02:51.570 --> 01:02:56.279
Rm 330: I think, yes, maybe one should really care about remote subject.

425
01:02:58.730 --> 01:03:01.159
Rm 330: Okay, thank you, thank you, Anna. Thank you very much.