AI 中文总结
本文构造了2+1维$S_3$量子双重格点模型，实现了电-磁自对偶性，分析了其拓扑相变，提出最小凝聚原理，且模型无符号问题可用于大规模数值模拟。
AI 中文摘要
$\boldsymbol{Z}_2$规范理论的电-磁自对偶性以半格点平移微观实现，可交换电荷与磁通量，是具有精确格点实现的对偶对称性的重要范例。我们构造了该结构的首个非阿贝尔推广：在张量积希尔伯特空间上的$S_3$量子双重$\boldsymbol{\textrm{D}}(S_3)$格点模型，其中非阿贝尔荷子$C$与通量子$F$的anyon置换对称性$\boldsymbol{Z}^{\textrm{em}}_2$通过格点平移实现。由此发现，该模型的锯齿形边界终止无需精细调谐即可实现由四临界点伊辛CFT描述的无能隙临界边缘态。体相存在三种独立的$\boldsymbol{Z}^{\textrm{em}}_2$保持玻色型微扰，可驱动$\boldsymbol{\textrm{D}}(S_3)$进入不同的有隙相。我们通过三种独立方法分析这些相变：范畴论anyon凝聚、微观格点哈密顿量及陈-西蒙斯-希格斯理论，三者结果一致，形成统一图景。这些例子催生了最小凝聚原理：增殖玻色型anyon通常会驱动包含它的最小可凝聚代数发生凝聚，与对称性相关的凝聚体表现为简并真空，会自发破缺anyon置换对称性。我们的模型可推广至无限族自对偶二面体量子双重$\boldsymbol{\textrm{D}}(D_{2n})$。值得注意的是，每个模型均无符号问题，为非阿贝尔陈-西蒙斯-希格斯理论相的大规模数值探索打开了大门。
英文摘要
Electric-magnetic self-duality of the $\mathbb{Z}_2$ gauge theory, realized microscopically as a half-lattice-translation exchanging electric charge and magnetic flux, has been an influential example of a duality symmetry with an exact lattice realization. We construct the first non-Abelian generalization of this construction: a lattice model of the $S_3$ quantum double $\mathcal{D}(S_3)$ on a tensor product Hilbert space in which the $\mathbb{Z}^{\mathrm{em}}_2$ anyon-permutation symmetry, exchanging the non-Abelian chargeon $C$ and fluxon $F$, is realized via lattice translation. Consequently we find that the zigzag boundary termination of the model realizes, without fine-tuning, a gapless critical edge state described by the tetracritical Ising CFT. The bulk admits three independent $\mathbb{Z}_2^{\mathrm{em}}$-preserving bosonic perturbations, driving $\mathcal{D}(S_3)$ into distinct gapped phases. We analyze these transitions by three independent methods: category-theoretic anyon condensation, microscopic lattice Hamiltonians, and Chern-Simons-Higgs theory, which all agree, yielding a unified picture. These examples motivate a minimal-condensation principle: proliferating a bosonic anyon generically drives condensation of a minimal condensable algebra containing it, with symmetry-related condensates appearing as degenerate vacua that spontaneously break the anyon-permutation symmetry. Our model construction extends to an infinite family of self-dual dihedral quantum doubles $\mathcal{D}(D_{2n})$. Notably, each model is sign-problem-free, opening the door to large-scale numerical exploration of the phases of non-Abelian Chern-Simons-Higgs theories.
Comments10 pages, 2 figures, 18 pages of supplementary materials
