Papers › Classification of symmetry-enriched topological quantum spin liquids
Classification of symmetry-enriched topological quantum spin liquids
Weicheng Ye, Liujun Zou
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We present a systematic framework to classify symmetry-enriched topological quantum spin liquids in two spatial dimensions. This framework can deal with all topological quantum spin liquids, which may be either Abelian or non-Abelian, chiral or non-chiral. It can systematically treat a general symmetry, which may include both lattice symmetry and internal symmetry, may contain anti-unitary symmetry, and may permute anyons. The framework applies to all types of lattices, and can systematically distinguish different lattice systems with the same symmetry group using their Lieb-Schultz-Mattis anomalies. We apply this framework to classify U(1)_(2N) chiral states and non-Abelian Ising^((ν)) states enriched by a p6×SO(3) or p4×SO(3) symmetry, and ℤ_N topological orders and U(1)_(2N)×U(1)_(-2N) topological orders enriched by a p6m×SO(3)×ℤ₂ᵀ, p4m×SO(3)×ℤ₂ᵀ, p6m×ℤ₂ᵀ or p4m×ℤ₂ᵀ symmetry, where p6, p4, p6m and p4m are lattice symmetries, while SO(3) and ℤ₂ᵀ are spin rotation and time reversal symmetries, respectively. In particular, we identify symmetry-enriched topological quantum spin liquids that are not easily captured by the usual parton-mean-field approach, including examples with the familiar ℤ₂ topological order.
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