非阿贝尔任意子凝聚：一种路径积分蒙特卡洛方法
Non-Abelian Anyon Condensation: a Path-Integral Monte Carlo Approach
- Technical University of Munich（慕尼黑工业大学）
- Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与技术中心）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出无符号路径积分蒙特卡洛框架，研究非阿贝尔任意子凝聚，以S3群为例揭示一级相变与禁闭机制，统一描述广义对称性破缺。
AI中文摘要：
在微观量子模型中，用在大尺度下仍可处理的数值方法描述非阿贝尔拓扑序的转变是困难的。我们通过将单链微扰按非可逆电和磁1-形式对称性组织起来，这些对称性使不同的任意子种类增殖，从而为Kitaev量子双体$\mathcal D(G)$开发了一个无符号路径积分框架。对于任何有限群$G$，一个精确的$\textit{物质化}$等距引入了顶点自由度，并将仅含链的模型映射到$G$规范-希格斯理论上。此外，不动点的1-形式对称性使我们能够定义广义的Fredenhagen-Marcu序参量，当相应的任意子凝聚时，这些序参量变为有限值。对于$G = S_3$，量子蒙特卡洛模拟表明，增殖一个非阿贝尔电任意子驱动一个一级相变，其中所有非平凡电任意子都凝聚。在纯磁极限下，该模型简化为$(2+1)$维纯$G$规范理论；对于$G=S_3$，它表现出一个一级禁闭转变，通过Wilson环面积律的开始和涌现磁1-形式对称性的恢复来诊断。这些结果为非阿贝尔任意子凝聚、禁闭和广义对称性破缺提供了一个统一的数值框架。
英文摘要：
Transitions out of non-Abelian topological order are difficult to describe in microscopic quantum models with numerical methods that remain tractable at large scales. We develop a sign-free path-integral framework for Kitaev quantum doubles $\mathcal D(G)$ by organizing single-link perturbations in terms of non-invertible electric and magnetic 1-form symmetries that proliferate distinct anyon species. For any finite group $G$, an exact $\textit{matterization}$ isometry introduces vertex degrees of freedom and maps the link-only model onto a $G$ gauge--Higgs theory. Furthermore, the 1-form symmetries of the fixed point allow us to define generalized Fredenhagen--Marcu order parameters that become finite when the corresponding anyons condense. For $G = S_3$, quantum Monte Carlo simulations show that proliferating a non-Abelian electric anyon drives a first-order transition in which all nontrivial electric anyons condense. In the purely magnetic limit, the model reduces to a $(2+1)$D pure $G$ gauge theory; for $G=S_3$, it exhibits a first-order confinement transition, diagnosed by the onset of a Wilson-loop area law and the restoration of an emergent magnetic 1-form symmetry. These results provide a unified numerical framework for non-Abelian anyon condensation, confinement, and generalized symmetry breaking.
