Topological phases of one-dimensional fermions: An entanglement point of view

The effect of interactions on topological insulators and superconductors remains, to a large extent, an open problem. Here, we describe a framework for classifying phases of one-dimensional interacting fermions, focusing on spinless fermions with time-reversal symmetry and particle number parity conservation, using concepts of entanglement. In agreement with an example presented by L. Fidkowski and A. Kitaev [Phys. Rev. B 81, 134509 (2010)], we find that in the presence of interactions there are only eight distinct phases which obey a ${\mathbb{Z}}_{8}$ group structure. This is in contrast to the $\mathbb{Z}$ classification in the noninteracting case. Each of these eight phases is characterized by a unique set…