Building 1D lattice models with $G$-graded fusion category

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Abstract
We construct a family of one-dimensional (1D) quantum lattice models based on G G -graded unitary fusion category \mathcal{C}_G ???? G . This family realize an interpolation between the anyon-chain models and edge models of 2D symmetry-protected topological states, and can be thought of as edge models of 2D symmetry-enriched topological states. The models display a set of unconventional global symmetries that are characterized by the input category \mathcal{C}_G ???? G . While spontaneous symmetry breaking is also possible, our numerical evidence shows that the category symmetry constrains the models to the extent that the low-energy physics has a large likelihood to be gapless.
Funding Information
  • Chinese University of Hong Kong (4053416)
  • National Natural Science Foundation of China (12222416)
  • National Natural Science Foundation of China (N-CUHK427/18)
  • Research Grants Council, University Grants Committee (11300819)
  • Research Grants Council, University Grants Committee (14302021)
  • Research Grants Council, University Grants Committee (17311322)

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