The effect of interactions on 2D fermionic symmetry-protected topological phases with Z2 symmetry

TL;DR

This paper investigates how interactions influence 2D fermionic SPT phases with Z2 symmetry, revealing a reduction in classification from Z to Z8 and identifying protected edge modes in nontrivial phases.

Contribution

It demonstrates that interactions reduce the classification of Z2 symmetric 2D fermionic SPT phases from Z to Z8 and establishes the existence of protected edge modes in these phases.

Findings

Classification reduces from Z to Z8 with interactions

Identifies at least 8 distinct Ising superconductor types

Proves protected edge modes in nontrivial phases

Abstract

We study the effect of interactions on 2D fermionic symmetry-protected topological (SPT) phases using the recently proposed braiding statistics approach. We focus on a simple class of examples: superconductors with a Z2 Ising symmetry. Although these systems are classified by Z in the noninteracting limit, our results suggest that the classification collapses to Z8 in the presence of interactions -- consistent with previous work that analyzed the stability of the edge. Specifically, we show that there are at least 8 different types of Ising superconductors that cannot be adiabatically connected to one another, even in the presence of strong interactions. In addition, we prove that each of the 7 nontrivial superconductors have protected edge modes.