Categorical Landau Paradigm for Gapped Phases

2023/10/05 by Lakshya Bhardwaj, Bhardwaj, Lakshya, Lea E. Bottini +5 · 16 citations
Chemistry · Engineering · Materials Science · #Category Theory (math.CT) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Liquid Crystal Research Advancements #Molecular spectroscopy and chirality #Optical Polarization and Ellipsometry #Strongly Correlated Electrons (cond-mat.str-el)

paper · pdf · doi:10.48550/arxiv.2310.03786

openalex publication_date 2023/10/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

Abstract

We propose a unified framework to classify gapped infra-red (IR) phases with categorical symmetries, leading to a generalized, categorical Landau paradigm. This is applicable in any dimension and gives a succinct, comprehensive, and computationally powerful approach to classifying gapped symmetric phases. The key tool is the symmetry topological field theory (SymTFT), which is a one dimension higher TFT with two boundaries, which we choose both to be topological. We illustrate the general idea for (1+1)d gapped phases with categorical symmetries and suggest higher-dimensional extensions.

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