PHY576 Understanding Topological Phases of Matter from Toy Models

The exploration of topological phases of matter is to a large extend guided by a range of exactly soluble toy models that illustrate the physics at play. In this course, we will study classic models such as the Su-Schrieffer-Heeger model, Kitaev’s Majorana chain, and the toric code. We will use them to understand topological band insulators and the basic concepts of topological order in systems with anyon excitations. The presentation will be as self-contained as possible with an emphasis on explicit derivations of all the relevant properties.

Lecture Notes (PDF, 2 MB)