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

• URL: http://arxiv.org/abs/2301.06416v1
• Date: Mon, 16 Jan 2023 13:16:50 GMT
• Title: Building 1D lattice models with $G$-graded fusion category
• Authors: Shang-Qiang Ning, Bin-Bin Mao and Chenjie Wang
• Abstract summary: Family of 1D quantum lattice models based on $G$-graded fusion category $mathcalC_G$. The models display a set of unconventional global symmetries characterized by the input category $mathcalC_G$.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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