Guidelines

Choose a research paper (suggested papers below) related to the topics covered in the class for a final presentation and paper.

The final presentation will be 10mins + 5mins for questions. The presentation should clearly explain what problem the paper is trying to solve and why it is important. The goal is to teach your classmates, as well as to demonstrate your understanding.

The presentations will be held over Zoom. You must present slides (no virtual chalk talks).

The final paper should not exceed 4 pages. The goal of the paper is to explain the topic in your own words. You are welcome to consult other references. The paper is due at our exam time (Fri, May 15, 11:15am.) You are welcome to submit the paper earlier.

You are welcome to suggest a topic not on the list below, although it is subject to my approval. The paper should be classic or foundational.

I will write names next to the papers as they are taken.

Final presentation schedule

All students are expected to attend all talks! Presenters please have your slides ready on your computer.

Tues, May 5, 10am: Hiroke Sukeno, Xuance Jiang, Yue Chen, Andrei Grekov, Leonid Korneev

Thurs, May 7, 10am: David Frenklakh, Yichul Choi, Dimitrios Athanasakos, Mikhail Litvinov, Kedarsh Kaushik

Fri, May 15, 11:15am: Shuo Tao, Hongyi Huang, Zijian Zhou, Jiacheng Sun, Sergey Alekseev, Hao-Lan Xu

Topics

(Zijian) Mermin-Wagner theorem: https://journals.aps.org/prl/pdf/10.1103/PhysRevLett.17.1133

(Yichul) Jackiw-Rebbi model (solitons at domain wall): https://journals.aps.org/prd/abstract/10.1103/PhysRevD.13.3398

(Leonid) SSH model (solitons in polyacetylene): https://journals.aps.org/prb/pdf/10.1103/PhysRevB.22.2099

(Xuance) Haldane model (quantum Hall effect without Landau levels): https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.61.2015

(Hao-Lan) “Gang of four” scaling theory of localization: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.42.673

(Dimitrios) Anderson localization: https://journals.aps.org/pr/pdf/10.1103/PhysRev.109.1492

Many body localization: https://arxiv.org/pdf/cond-mat/0602510.pdf

Goldstone modes: https://journals.aps.org/pr/pdf/10.1103/PhysRev.127.965

(Hiroki) AKLT model (valence bond ground states in antiferromagnets): https://journals.aps.org/prl/pdf/10.1103/PhysRevLett.59.799

Rokhsar-Kivelson model (resonating valence bond solid): https://journals.aps.org/prl/pdf/10.1103/PhysRevLett.61.2376

Higgs mechanism: https://journals.aps.org/prl/pdf/10.1103/PhysRevLett.13.508 (application to superconductivity by Anderson: https://journals.aps.org/pr/abstract/10.1103/PhysRev.130.439)

Kubo formula and applications: https://journals.jps.jp/doi/10.1143/JPSJ.12.570

Topological defects in order parameters: https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.51.591

(Hongyi) Bosonization and the Luttinger Liquid: Sec. 4 of https://arxiv.org/pdf/cond-mat/9807366.pdf

(Yue) Effective field theory for fractional quantum Hall: https://journals.aps.org/prl/pdf/10.1103/PhysRevLett.62.82

(Jiacheng) Quantum Hall effect on a lattice (TKNN): https://journals.aps.org/prl/pdf/10.1103/PhysRevLett.49.405

Laughlin theory of quantum Hall effect: https://journals.aps.org/prl/pdf/10.1103/PhysRevLett.50.1395

(Kedarsh) Z2 Topological insulator: https://journals.aps.org/prl/pdf/10.1103/PhysRevLett.95.226801, https://journals.aps.org/prl/pdf/10.1103/PhysRevLett.95.146802

(Sergey) Kitaev model for Majorana fermions in quantum wires: https://arxiv.org/pdf/cond-mat/0010440.pdf

(Mikhail) Kitaev periodic table for topological insulators and superconductors: https://arxiv.org/pdf/0901.2686.pdf