Effect of strong interactions on the classification of fermionic phases

Determine how the established classification of zero-temperature phases of non-interacting fermionic systems changes when arbitrarily strong interactions are allowed, with the goal of identifying the interaction-stable classification of phases (including invertible phases) beyond the free-fermion framework.

Background

The periodic table of topological insulators and superconductors provides a comprehensive classification of non-interacting fermionic phases at zero temperature. However, introducing interactions can collapse or refine this classification, and understanding the interaction-stable classification is a central problem in condensed matter theory.

This paper focuses on invertible (short-range entangled) phases in two dimensions and defines indices intended to capture interaction-robust invariants. Resolving how interactions alter the full classification would contextualize these indices within a complete interacting-phase framework.