Topology and New Kinds of Order in Condensed Matter Physics (PH2246)
Summer 2017
Frank Pollmann
Lectures (Theory seminar room):
Monday 10:00 - 12:00
Wednesday 10:00 - 12:00
Outline:
Introduction
(1) Landau Theory, Kosterlitz Thouless transition [PDF]
(2) Quantum Phases of matter, second quantization, quantum-Ising model [PDF]
Quantum Hall Effect
(3) Phenomenology, Disorder, Laughlin’s argument, Berry Phase, TKKN [PDF]
Topological Band structures
(4) Su-Schrieffer-Heeger Model: Edge modes, topological invariant [PDF]
(5) Haldane model [PDF, ipynb]
(6) 2D TR-invariant topological insulators [PDF]
(7) 3D TR-invariant topological insulators [PDF]
(8) 3D Weyl semimetals [PDF]
(9) Topological superconductors: Kitaev chain [PDF]
(10) Periodic table of topological band structures [PDF]
Interacting Symmetry Protected Topological Phases
(11) Quantum-Many Body Systems and Entanglement [PDF]
(12) Matrix-Product States [PDF]
(13) Symmetry Protected Topological Phases [PDF]
Topological order
(14) Fractional quantum Hall effect [PDF]
(15) Toric code and topological entanglement [PDF]
(16) Quantum Spin Liquids [PDF]
(17 )Topological quantum computing [PDF]
Fractionalization and emergent electrodynamics
3D Spin ice and monopoles
[The files are protected by a password. I'll mail the password on request.]
Tutorials (C.3201, tutor room)
Monday 8:00 - 10:00
Literature:
Quantum Field Theory of Many-Body Systems, X.-G. Wen, Oxford.
Graduate Text Lecture notes by John Preskill: www.theory.caltech.edu/~preskill/ph219/topological.pdf.
Lecture notes by Alexei Kitaev and Chris Laumann: arxiv.org/pdf/0904.2771v1.pdf
Review article by Chetan Nayak et al.: arxiv.org/pdf/0707.1889v2.pdf.