Interaction effects on the classification of non-interacting fermionic phases

Determine how the established zero-temperature classification of phases of non-interacting fermionic systems changes when arbitrarily strong interactions are allowed, with particular attention to short-range entangled (invertible) phases where a complete interacting classification may be tractable.

Background

The paper begins by recalling that the classification of phases of non-interacting fermionic systems at zero temperature is well understood, referencing prior work on the periodic table of topological insulators and superconductors. However, once interactions are introduced, the free-fermion classification may collapse or refine, and a general interacting classification is largely unknown.

The authors note that while the fully general problem appears intractable, progress may be possible for short-range entangled (invertible) phases, motivating their construction of an index intended to serve as an invariant for such phases without assuming additional symmetries.