Course Meeting Times
Lectures: 2 sessions / week, 1.5 hours / session
Prerequisites
8.033 Relativity, 8.05 Quantum Physics II, 8.08 Statistical Physics II, and 8.231 Physics of Solids I
Description
This graduate-level course covers the quantum effect in solids, such as the phenomena related to topological phases of matter. We cover the following topics:
- Semiclassical approach
- Emerging dynamics of quasiparticles (beyond Newton’s Law)
- Geometric phase, Chern number, and fiber bundle
- Quantum Hall insulator—a topological phase of matter
- Interaction bosonic superfluid
- Quantum 1D Ising model and symmetry breaking
- Critical point in 1D Ising model and its dual free fermion model
- Topological superconductors
- Half-qubits—Majorana zero modes
- K-theory for symmetry protected topological phases of free fermions
- \(Z_2\) topological order for 2D interacting bosons
- Emergent fermions and string operators
- Topological order and long range entanglement
- Higher category theory for topological excitations
Textbook and Notes
There is no assigned textbook for this course. Instead, detailed lecture notes are provided in the form of slide presentations used in class.
Requirements
There are weekly problem set assignments, due on Thursday at lecture. There is also a term paper.
