A pedestrian’s guide to the topological phases of free fermions - Schindler,F (SciPost Physics Lecture Notes, 2026)
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 manyof the models we work with are non-interacting. We start out with symmetry protectedtopological (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 changesin presence of spinless time-reversal symmetry. We close by perturbatively checking which of the 1D topological phases we had found are stable to interactions.