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

Ari M. Turner, Frank Pollmann, and Erez Berg
Phys. Rev. B 83, 075102 – Published 8 February 2011

Abstract

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 Z8 group structure. This is in contrast to the 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.

  • Figure
  • Received 29 August 2010

DOI:https://doi.org/10.1103/PhysRevB.83.075102

©2011 American Physical Society

Authors & Affiliations

Ari M. Turner

  • Department of Physics, University of California, Berkeley, California 94720, USA

Frank Pollmann

  • Department of Physics, University of California, Berkeley, California 94720, USA and
  • Institute of Physics, Academia Sinica, Taipei 11529, Taiwan

Erez Berg

  • Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA

See Also

Topological phases of fermions in one dimension

Lukasz Fidkowski and Alexei Kitaev
Phys. Rev. B 83, 075103 (2011)

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Vol. 83, Iss. 7 — 15 February 2011

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