标题： 具有 categorical 对称性的能隙相的 (2+1)d 格点模型和张量网络 显示英文标题

标题： (2+1)d Lattice Models and Tensor Networks for Gapped Phases with Categorical Symmetry

摘要： 具有融合2-范畴对称性的2+1维量子场论中的能隙相在近期通过对称拓扑场论（SymTFT）方法（arXiv:2408.05266, arXiv:2502.20440）被分类和刻画。本文中，我们为所有此类能隙相提供了一个系统的晶格模型构造方法。具体来说，我们考虑“全玻色子类型”的融合2-范畴对称性，这些对称性都可以通过广义规范化的手段从0形式对称群 $G$ （可能带有't Hooft异常）获得——即通过与一个 $H$ -对称的拓扑场论堆叠，并规范一个子群 $H$ 。连续统分类直接决定了晶格数据，例如确定对称范畴的广义规范化以及指定能隙相的数据。我们构建了适用于任何此类对称性的非手征能隙相的交换投影算符哈密顿量和基态。我们还用张量网络描述了基态。鉴于本文篇幅较长，我们包含了一个自包含的总结部分，概述了主要结果和例子。 显示英文摘要

摘要： Gapped phases in 2+1 dimensional quantum field theories with fusion 2-categorical symmetries were recently classified and characterized using the Symmetry Topological Field Theory (SymTFT) approach arXiv:2408.05266, arXiv:2502.20440. In this paper, we provide a systematic lattice model construction for all such gapped phases. Specifically, we consider ``All boson type" fusion 2-category symmetries, all of which are obtainable from 0-form symmetry groups $G$ (possibly with an 't Hooft anomaly) via generalized gauging--that is, by stacking with an $H$-symmetric TFT and gauging a subgroup $H$. The continuum classification directly informs the lattice data, such as the generalized gauging that determines the symmetry category, and the data that specifies the gapped phase. We construct commuting projector Hamiltonians and ground states applicable to any non-chiral gapped phase with such symmetries. We also describe the ground states in terms of tensor networks. In light of the length of the paper, we include a self-contained summary section presenting the main results and examples.