10/7/20








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 502512, 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 2111 (2006). ``Kitaev quantum spin liquid: concept and materialization", Hide Takagi, Tomohiro Takayama, George Jackeli and Giniyat Khaliullin, arXiv 1903.08081, Nature Review Physics, 1, 264280 (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 Tlinear resistivty and Planckian dissipation in overdoped cuprates", A. Legros et al, Nature Physics, 15, 142147 (2019). 

Exercise 2: the FQHE (due
30th Oct) Exercise 3: Kitaev Model
with Jordan Wigner transformation (Return to top) 

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 1.403.00 on M and W) to the tentative plan of Wednesday 10.2011.40am, Friday 1.403.00pm. Office hour: To be arranged. Assessment: I anticipate four or five take home exercises and one takehome final. I want to encourage an interactive class and will take this into account when grading! (Return to top) 

(Return to top) Schedule:
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