Classification of gapped symmetric phases in one-dimensional spin systems
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Chen-2011-Classification of ga.pdf
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Author(s)
Chen, Xie
Gu, Zheng-Cheng
Wen, Xiao-Gang
Date Issued
January 2011
Journal
Physical Review B
Publisher
American Physical Society
Citation
Chen, Xie, Zheng-Cheng Gu, and Xiao-Gang Wen. “Classification of Gapped Symmetric Phases in One-dimensional Spin Systems.” Physical Review B 83.3 (2011) : 035107. © 2011 American Physical Society
Version
Final published version
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.
MIT Department
Massachusetts Institute of Technology. Department of Physics
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DOI of Published Version
https://doi.org/10.1103/PhysRevB.83.035107
