Topological Quantum Many-Body Physics

The goal of this course is to gain a thorough understanding of topological concepts in modern quantum many-body physics. You aquire the mathematical tools needed to describe topological quantum phases, understand the physical features that characterize these systems, and learn about potential applications.

Topological phases of non-interacting fermions:

- Integer quantum Hall effect
- Berry connection, Berry holonomy, Chern number
- Anomalous quantum Hall effect (Haldane model)
- Quantum spin Hall effect, topological insulators (Kane-Mele model)
- Pfaffian topological invariant
- Winding numbers, sublattice symmetry, edge modes (SSH model)
- Topological superconductivity (Majorana chain)
- Tenfold way and periodic table of topological insulators/superconductors
- Effects of interactions
- Topological bands in classical systems (topological metamaterials ...)

Symmetry-protected topological phases of interacting bosons:

- Tensor network states, matrix product states, PEPS
- Projective representations and (twisted) cohomology groups
- Classification of bosonic topological phases in one dimension
- Haldane chain and AKLT model

Intrinsic topological order and long-range entanglement:

- Statistics of indistinguishable particles in 2+1 dimensions (Braid group)
- Toric code (anyonic excitations, top. entanglement entropy ...)
- Topological quantum memories
- Fibonacci anyons
- String-net condensates
- Topological quantum computation (non-abelian anyons, braiding, fusion ...)
- Mathematical framework:
- Modular tensor categories, pentagon & hexagon relations,
- quantum dimension, topological spin ....
- Application to foundational questions of high-energy physics (fermions ...)

M.Sc. Physik, M.Sc. Physics

Dr. Nicolai Lang

Wahlpflichtmodul Ergänzung / Semicompulsory module

V57.05

4

9

SS25

M.Sc. Physik, M.Sc. Physics

English

All rights reserved

Nicolai Lang

0711 685 65215

nicolai.lang@itp3.uni-stuttgart.de

Unlimited

You can join this course directly.

Unlimited

10. Apr 2025 - 18. Jul 2025

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