A dualization approach to the Ground State Subspace Classification of Abelian Higher Gauge Symmetry Models

• URL: http://arxiv.org/abs/2207.09522v2
• Date: Fri, 01 Nov 2024 20:52:36 GMT
• Title: A dualization approach to the Ground State Subspace Classification of Abelian Higher Gauge Symmetry Models
• Authors: J. Lorca Espiro,
• Abstract summary: Ground state degeneracy and entanglement entropy were thoroughly studied, but the classification of the ground state space remained obscure. We show that the ground state space is classified by a $H0 (C,G) times H_0 (C,G)$ group, where $H0(C,G)$ is the $0$-th cohomology.
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• Abstract: In the literature, abelian higher gauge symmetry models are shown to be valid in all finite dimensions and exhibit the characteristic behavior of SPT phases models. While the ground state degeneracy and the entanglement entropy were thoroughly studied, the classification of the ground state space still remained obscure. Based on differentio-geometric approach and, anticipating the notation of the current paper, if $\left( C_{\bullet} , \partial^C_{\bullet} \right)$ is the chain complex associated to the geometrical content of these models, while $\left( G_{\bullet} , \partial^G_{\bullet} \right)$ is its symmetries counterpart, we show that the ground state space is classified by a $H^0 (C,G) \times H_0 (C,G)$ group, where $H^0(C,G)$ is the $0$-th cohomology and $H_0 (C,G)$ is the corresponding $0$-th homology group with coefficients in the chain complex.

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