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Classification of gapped symmetric phases in one-dimensional spin systems

Xie Chen, Zheng-Cheng Gu, and Xiao-Gang Wen
Phys. Rev. B 83, 035107 – Published 13 January 2011

Abstract

Quantum many-body systems divide into a variety of phases with very different physical properties. The questions of what kinds of phases exist and how to identify them seem hard, especially for strongly interacting systems. Here we make an attempt to answer these questions for gapped interacting quantum spin systems whose ground states are short-range correlated. Based on the local unitary equivalence relation between short-range-correlated states in the same phase, we classify possible quantum phases for one-dimensional (1D) matrix product states, which represent well the class of 1D gapped ground states. We find that in the absence of any symmetry all states are equivalent to trivial product states, which means that there is no topological order in 1D. However, if a certain symmetry is required, many phases exist with different symmetry-protected topological orders. The symmetric local unitary equivalence relation also allows us to obtain some simple results for quantum phases in higher dimensions when some symmetries are present.

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  • Received 23 August 2010

DOI:https://doi.org/10.1103/PhysRevB.83.035107

© 2011 American Physical Society

Authors & Affiliations

Xie Chen1, Zheng-Cheng Gu2, and Xiao-Gang Wen1,3

  • 1Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
  • 2Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106, USA
  • 3Institute for Advanced Study, Tsinghua University, Beijing, 100084, People’s Republic of China

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Issue

Vol. 83, Iss. 3 — 1 January 2011

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