Building 1D lattice models with G-graded fusion category

2023/01/16 by Shang-Qiang Ning, Ning, Shang-Qiang, Bin-Bin Mao +3
Physics and Astronomy · #Atomic and Subatomic Physics Research #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Physics of Superconductivity and Magnetism #Quantum Physics (quant-ph) #Quantum many-body systems #Statistical Mechanics (cond-mat.stat-mech) #Strongly Correlated Electrons (cond-mat.str-el)

paper · pdf · doi:10.48550/arxiv.2301.06416

openalex publication_date 2023/01/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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