阿贝尔高阶规范对称性模型基态子空间分类的对偶化方法
A dualization approach to the Ground State Subspace Classification of Abelian Higher Gauge Symmetry Models
AI总结：
针对阿贝尔高阶规范对称性模型基态空间分类不明的问题，本文基于微分几何方法与对偶化思路，证明其基态空间可由第0阶上同调与同调群的直积群分类，完善了SPT相相关模型的理论研究。
摘要：
现有文献表明，阿贝尔高阶规范对称性模型在所有有限维度下均成立，且展现出SPT相模型的特征行为。尽管基态简并度与纠缠熵已得到深入研究，但基态空间的分类问题仍不明确。基于微分几何方法，并采用本文的记号体系：若$(C_{\bullet}, \partial^C_{\bullet})$是与这些模型几何内容相关的链复形，而$(G_{\bullet}, \partial^G_{\bullet})$是其对称性对应的链复形，我们证明基态空间可由$H^0(C,G) \times H_0(C,G)$群分类，其中$H^0(C,G)$是第0阶上同调群，$H_0(C,G)$是相应的以该链复形为系数的第0阶同调群。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
