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

TL;DR

This paper constructs 1D quantum lattice models based on $G$-graded fusion categories, bridging anyon chains and edge states of 2D topological phases, revealing symmetry constraints that favor gapless low-energy physics.

Contribution

It introduces a new class of 1D models based on $G$-graded fusion categories, connecting topological and symmetry-protected phases with unconventional symmetries.

Findings

Models interpolate between anyon chains and 2D edge states

Category symmetry constrains models towards gapless phases

Numerical evidence supports the prevalence of gapless low-energy physics

Abstract

We construct a family of one-dimensional (1D) quantum lattice models based on $G$-graded unitary fusion category $\mathcal{C}_G$. 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 $\mathcal{C}_G$. While spontaneous symmetry breaking is also possible, our numerical evidence shows that the category symmetry constrains the the models to the extent that the low-energy physics has a large likelihood to be gapless.