Physics – Condensed Matter – Strongly Correlated Electrons
Scientific paper
2010-08-25
Phys. Rev. B 83, 075102 (2011)
Physics
Condensed Matter
Strongly Correlated Electrons
12 pages, 1 figure; journal ref. added
Scientific paper
10.1103/PhysRevB.83.075102
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 Fidkowski \emph{et. al.} (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 non-interacting 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.
Berg Erez
Pollmann Frank
Turner Ari M.
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