D54.00006. Lattice models that realize Zn-1-symmetry protected topological states for even n

Presented by: Lokman Tsui


We study the lattice model of Zn-1-symmetry protected topological states (1-SPT) in 3+1D for even n. We write down an exactly soluble lattice model and study its boundary transformation. On the boundary, we show the existence of anyons with non-trivial self-statistics. For the n=2 case, where the bulk classification is given by an integer m mod 4, we show that the boundary can be gapped with double semion topological order for m=1 and toric code for m=2. The bulk ground state wavefunction amplitude is given in terms of the linking numbers of loops in the dual lattice. Our construction can be generalized to arbitrary 1-SPT protected by finite unitary symmetry. *LT is supported by the Croucher Fellowship for Postdoctoral Research. XGW is partially supported by NSF Grant No. DMS-1664412.


  • Lokman Tsui
  • Xiao-Gang Wen


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