Classification of gapped symmetric phases in one-dimensional spin systems

By Xie Chen, Z. Gu, X. Wen. 2010

733 citations recorded by the source corpus.

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.

Subfields: Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/0e2db33fe35a4a5dae2cbe643146af20dead2c58

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In Atomic and Molecular Physics, and Optics

Citations in the corpus

Gapless Topological Phases and Symmetry-Enriched Quantum Criticality (2019, background): “[3] Xie Chen, Zheng-Cheng Gu, and Xiao-Gang Wen, “Classification of gapped symmetric phases in one-dimensional spin systems,” Phys.”
Superconductivity from valley fluctuations and approximate SO(4) symmetry in a weak coupling theory of twisted bilayer graphene (2018, background): “[94] Xie Chen, Zheng-Cheng Gu, and Xiao-Gang Wen, “Classification of gapped symmetric phases in onedimensional spin systems,” Phys.”
Measurement as a Shortcut to Long-Range Entangled Quantum Matter (2022, background): “More recently, it was found that performing measurements on SRE states in certain symmetry-protected-topological (SPT) phases [5, 6] can lead to a large class of LRE states in topologically ordered phases [7, 8].”
Topological Phases Protected by Point Group Symmetry (2016, methodology): “Such phases are known to obey a Z2 classification [6,7,10,11], a conclusion reproduced by our analysis here.”
Quantum spin liquid states (2016, background): “…Sσ describes two plausible phases, the weak coupling phase, in which the ground state is antiferromagnetically ordered, 1 For S = 1 chains, the S = 1/2 end states are protected by a weaker Z2 × Z2 symmetry (Chen et al., 2011a,b). and the strong coupling phase, in which the ground state is gapped.”
Stability of Frustration-Free Hamiltonians (2011, methodology): “Motivated by this line of research and the larger question of the classification of quantum phases [3,9,41,43], we present here a generalization of the result by Bravyi et al.”