Introduction to some of the simplest topological phases of matter

• URL: http://arxiv.org/abs/2509.19320v1
• Date: Fri, 12 Sep 2025 15:56:39 GMT
• Title: Introduction to some of the simplest topological phases of matter
• Authors: Frank Schindler,
• Abstract summary: We focus on a many-body perspective, even if many of the models we work with are non-interacting.<n>We look at fermion topological phases that don't even need a symmetry = topological superconductors.<n>We close by perturbatively checking which of the 1D topological phases we had found are stable to interactions.
• Score: 0.20305676256390937
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 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.

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