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

2011; American Physical Society; Volume: 83; Issue: 7 Linguagem: Inglês

10.1103/physrevb.83.075102

1550-235X

Ari M. Turner, Frank Pollmann, Erez Berg,

Advanced Condensed Matter Physics

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 of bulk invariants, related to the transformation laws of its entanglement (Schmidt) eigenstates under symmetry operations, and has a characteristic degeneracy of its entanglement levels. If translational symmetry is present, the number of distinct phases increases to 16.