Topology and New Kinds of Order in Condensed Matter Physics (PH2246)
Summer 2018 

Lecturer: Lecturer: Frank Pollmann

Lectures (Theory seminar room):Monday 10:00 - 12:00Wednesday 10:00 - 12:00 Tutorials (C.3201, Tutorraum):Friday 8:00 - 10:00

Final Exam: Jul. 9 2017 / Jul. 24th 2017 [PDF]

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] [PDF]

Topological Band structures
(4) Su-Schrieffer-Heeger Model: Edge modes, topological invariant [PDF]
(5) Haldane model [PDF] [Haldane.py]
(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]

Topological order 
(11) Fractional quantum Hall effect [PDF]
(12) Quantum spin systems and entanglement [PDF]
(13) Toric code and anyons [PDF]
(14) A glimpse at topological quantum computing [PDF]
(15) Quantum Spin Liquids [PDF]

Interacting Symmetry Protected Topological Phases 

(16) Symmetry Protected Topological Phases in 1D [PDF] [PDF]
(17) Symmetry Protected Topological Phases in 2D [PDF]

Fractionalization and emergent electrodynamics 
(17) 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: http://www.theory.caltech.edu/~preskill/ph219/topological.pdf.
Lecture notes by Alexei Kitaev and Chris Laumann: http://arxiv.org/pdf/0904.2771v1.pdf
Review article by Chetan Nayak et al.: http://arxiv.org/pdf/0707.1889v2.pdf.