Lieb-Schultz-Mattis theorem for quasitopological systems

Michael Freedman, Chetan Nayak, and Kirill Shtengel
Phys. Rev. B 78, 174411 – Published 11 November 2008

Abstract

In this paper we address the question of the existence of a spectral gap in a class of local Hamiltonians. These Hamiltonians have the following properties: their ground states are known exactly; all equal-time correlation functions of local operators are short-ranged; and correlation functions of certain nonlocal operators are critical. A variational argument shows gaplessness with ωk2 at critical points defined by the absence of certain terms in the Hamiltonian, which is remarkable because equal-time correlation functions of local operators remain short ranged. We call such critical points, in which spatial and temporal scaling are radically different, quasitopological. When these terms are present in the Hamiltonian, the models are in gapped topological phases which are of special interest in the context of topological quantum computation.

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  • Received 31 August 2005

DOI:https://doi.org/10.1103/PhysRevB.78.174411

©2008 American Physical Society

Authors & Affiliations

Michael Freedman1, Chetan Nayak1,2, and Kirill Shtengel3,4,*

  • 1Microsoft Research, Station Q, CNSI Building, University of California, Santa Barbara, California 93106, USA
  • 2Department of Physics, University of California, Santa Barbara, California 93106, USA
  • 3Department of Physics and Astronomy, University of California, Riverside, California 92521, USA
  • 4California Institute of Technology, Pasadena, California 91125, USA

  • *kirill.shtengel@ucr.edu

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Vol. 78, Iss. 17 — 1 November 2008

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