Building 1D lattice models with G-graded fusion category

Abstract

We construct a family of one-dimensional (1D) quantum lattice models based on Ggraded unitary fusion category CG. 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 CG. 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.