In this section
@article{Schindler:2026:10.21468/SciPostPhysLectNotes.122,
author = {Schindler, F},
doi = {10.21468/SciPostPhysLectNotes.122},
journal = {Scipost Physics Lecture Notes},
title = {A pedestrian’s guide to the topological phases of free fermions},
url = {http://dx.doi.org/10.21468/SciPostPhysLectNotes.122},
volume = {122},
year = {2026}
}
TY - JOUR
AB - 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 superconductors, 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.
AU - Schindler,F
DO - 10.21468/SciPostPhysLectNotes.122
PY - 2026///
TI - A pedestrian’s guide to the topological phases of free fermions
T2 - Scipost Physics Lecture Notes
UR - http://dx.doi.org/10.21468/SciPostPhysLectNotes.122
VL - 122
ER -
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