10/7/20
Advanced Solid State Physics
Strange Metals and Fractionalization
603 Fall 2020
| Images | Texts |
Exercises |
Times of Course |
Syllabus outline |
Timetable |
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Flux attachment and the fractional quantization of Hall Effect in 2D heterojunctions. |
Fractionalization and Solitons in the Su Schrieffer Heeger Model |
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| The Kitaev Honeycomb
Model, showing the fractionalization of spins into
Majorana Fermions |
Linear resistivity of LaSrCuO4. A high temperature superconductor. |
Instructor: Piers Coleman, Room 268
If you have any questions about this course or the
homework, please do not hesitate to contact me via email
at : coleman@physics.rutgers.edu
Scope of Course. This course will introduce the
concepts of fractionalization and strange metals in solid
state physics. There will be a lot of
discussion and interaction. We will introduce
fractionalization in four classic contexts: the Su
Schrieffer Heeger model, the fractional Quantum Hall
Effect, the Kitaev Honeycomb model and the Kondo
Lattice. An important part of the course will be the
discussion of key scientific papers, both theory and
experiment. The last part of the course will discuss the
unsolved problem of strange metals, which develop in
strongly correlated metals near a quantum critical point,
discussing current experiment and theory on the topic.
"Soliton Excitations in Polyacetylene", W. P. Su, J. R. Schrieffer and A. J. Heeger, Phys. Rev. B 22, 2099 (1980)
``Topological Superconductors and Category Theory". by Titus Neupert and Andrei Bernevig.
``Modern Condensed Matter Physics " Chapters 12 and 16. Steve Girvin and Kun Yang, CUP (2019).
``Lectures on the Quantum Hall effect'', David Tong,
``Field Theories of Condensed Matter Physics", Chapter 13, pp 502-512, Eduardo Fradkin, CUP (2013).
``Topological Phases and Quantum Computation", Alexei Kitaev and Chris Laumann, arXiv:0904.2771.
``Anyons in an exactly solved model and Beyond", Alexei Kitaev, Annals of Physics 321 2-111 (2006).
``Kitaev quantum spin liquid: concept and materialization",
Hide Takagi, Tomohiro Takayama, George Jackeli and Giniyat Khaliullin, arXiv 1903.08081, Nature Review Physics, 1, 264-280 (2019).
"Heavy Fermions and the Kondo Lattice: a 21st Century Perspective", Piers Coleman, arXiv:1509.05769.
"Topological Approach to Luttinger's Theorem and the Fermi surface of a Kondo Lattice", Masaki Oshikawa, Phys. Rev. Lett., 84, 3370 (2000).
"Extending Luttinger's Theorem to Z2 fractionalized Phases", Arun Paramekanti and Ashwin Vishwanath, PRB 70, 245118 (2004).
"Universal T-linear resistivty and Planckian dissipation in overdoped cuprates", A. Legros et al, Nature Physics, 15, 142-147 (2019).
Exercises 603 (Return to top)
Exercise 1: the SSH Model (due
30th Sept)
Solution
Exercise 2: the FQHE (due
30th Oct)
Solution
Exercise 3: Kitaev Model
with Jordan Wigner transformation
Solution
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Times: The class will occur online. To avoid a clash with Many Body Physics 621, we will be moving the class away from the published time (originally
1.40-3.00 on M and W) to the tentative plan of Wednesday 10.20-11.40am, Friday 1.40-3.00pm.
Office hour: To be arranged.
Assessment: I anticipate four or five take home exercises and one take-home final. I want to encourage an interactive class and will take this into account when grading!
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Outline Here is the provisional outline.
- Solitons in the Su Schrieffer Heeger Model: an
elementary example of fractionalization
- The Fractional Quantum Hall Effect (mainly following
Girvin and Yang).
- Spin Fractionalization in the Kitaev Model
- Fractionalization in Heavy Fermions and the
Kondo Lattice. Oshikawa's Theorem.
- Strange Metals.
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Schedule:
Week |
Weds 10.20-12.00am |
Friday 1.40-3.00pm |
1.Sep 1-4 |
No Class |
No
Class |
2 Sep 7-11 |
First
Class of the Semester. Overview of Fractionalization. L1 notes |
The SSH Model L2 notes |
3 Sep 14-18 |
SSH Model L3 notes |
The Integer Quantum Hall Effect. Introduction L4 notes |
4 Sep 21-25 |
FQHE Integer QHE continued. FQHE Introduction. L5 notes |
FQHE Mechanical momentum and Guiding Centers. Electrons in the Lowest Landau Level. Haldane Pseudopotentials. Laughlin's Plasma Analogy. L6 Notes |
5 Sept 28-Oct 2 |
FQHE The Laughlin wavefunction. Anyons. The concept of fractional charge. L7 notes |
FQHE The concept of fractional Statistics Calculation of the statistical angle of Laughlin quasiparticles. Evidence for fractional statistics L8 notes |
6 Oct 5-9 |
FQHE Composite Fermions. L9 notes |
FQHE Chern Simons Theories L10 Notes |
7. Oct 12-16 |
FQHE Chern Simons Theories L11 Notes |
FQHE
wrap up. Class Discussion on FQHE and Chern Simons Theories Presentation by Roman Geiko on generalized Chern Simons Theories, his work with Greg Moore. Short Journal Club discussion on "Floating Topological Phases" by Devakul, Sondhi, Kivelson and Berg led by Pavel Volkov |
8. Oct 19-23 |
Kitaev Honeycomb Model L12 Notes |
Kitaev
Honeycomb Model L13 Notes |
9. Oct 26-30 |
Kitaev Honeycomb Model and Kitaev
Spin Liquids L14_Notes |
Real Kitaev Spin Liquids. (see L14 Notes) Introduction: The Kondo Lattice and Heavy Fermions. (see L15 Notes) |
10. Nov 2-6 |
The Kondo Lattice: From Anderson to Kondo L15 Notes |
The Kondo Lattice: Oshikawa's theorem. L16 Notes |
11. Nov 9-13 |
The Kondo Lattice: Oshikawa's theorem continued |
The Kondo Lattice: Large N Mean Field Approach L17 Notes |
12. Nov 16-20 |
Kondo Lattice: Large N Mean Field Approach |
Kondo Lattice: Heavy Fermion superconductivity L18 Notes |
13. Nov 23-27 |
No Class Thanksgiving |
No Class Thanksgiving |
14. Nov 30- Dec 4 |
Strange and Norma Metals contrasted. The Marginal Fermi liquid Phenomenology L19 Notes |
Strange Metals: fractionalization picture in RVB. The Ioffe-Larkin theory. L20 Notes |
15. Dec 7-11 |
12noon
Weds Class. Strange metals: Survey of Current Theories L21 Notes |
No Class. |
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