Classification of symmetry-protected phases for interacting fermions in two dimensions

Abstract

The authors deal with the fundamental problem of a rigorous classification of quantum topological phases. Here, they extend to the realm of interacting fermions in two dimensions techniques, developed for bosons, whereby they introduce extrinsic defects carrying symmetry fluxes into the topological phase. The result is a complete classification of symmetry-protected topological phases of interacting fermions in two dimensions. In addition, the classification of interacting fermion systems with time-reversal symmetry is also developed. The advances, reported here, are immediately relevant for the selection of reliable candidates for topologically protected storage and communication.