A pedestrian’s guide to the topological phases of free fermions
File(s)
Published version
Author(s)
Schindler, Frank
Type
Journal Article
Abstract
These lecture notes explain the classification of some simple fermionic topological phases of matter in a pedestrian manner, with an aim to be maximally pedagogical = doing things in excruciating detail. We focus on a many-body perspective, even if many
of the models we work with are non-interacting. We start out with symmetry protected
topological (SPT) phases of free fermions that are protected by U(1) symmetry = topological insulators. We then look at fermion topological phases that don’t even need a symmetry = topological super conductors, and explain how their classification changes
in presence of spinless time-reversal symmetry. We close by perturbatively checking which of the 1D topological phases we had found are stable to interactions.
of the models we work with are non-interacting. We start out with symmetry protected
topological (SPT) phases of free fermions that are protected by U(1) symmetry = topological insulators. We then look at fermion topological phases that don’t even need a symmetry = topological super conductors, and explain how their classification changes
in presence of spinless time-reversal symmetry. We close by perturbatively checking which of the 1D topological phases we had found are stable to interactions.
Date Issued
2026-01-01
Date Acceptance
2026-04-07
Citation
SciPost Physics Lecture Notes, 2026
ISSN
2590-1990
Publisher
SciPost
Journal / Book Title
SciPost Physics Lecture Notes
Volume
2026
Copyright Statement
Copyright F.Schindler. This work is licensed under the Creative Commons Attribution 4.0 International License. Published by the SciPost Foundation.
License URL
Publication Status
Published
Article Number
122
Date Publish Online
2026-05-01