2+1维拓扑有序超流体理论
Theory of Topologically Ordered Superfluids in 2+1 Dimensions
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中文总结 AI 辅助
本研究针对2+1维自发破缺电荷U(1)c对称性的玻色子系统，建立拓扑有序超流体的表征框架，通过双向规范映射编码其拓扑数据，还给出含非阿贝尔涡旋的实例，为相关研究提供理论基础。
中文摘要 AI 辅助
拓扑有序超流体（TOSF）支持退禁闭的有隙任意子激发，同时因戈德斯通模式而保持无隙。我们为具有自发破缺电荷U(1)c对称性的2+1维玻色子系统，开发了一套表征其拓扑数据的通用框架。规范U(1)c会将TOSF映射为受对偶U(1)dual对称性富集的有隙拓扑序，其霍尔电导为零；而规范U(1)dual则会恢复原TOSF。这种双向映射可利用对称性富集拓扑序的代数框架，系统编码TOSF的拓扑数据，包括凝聚电荷、退禁闭任意子内容及涡旋的拓扑性质。特别地，超流体涡旋具有与有隙任意子区残余离散对称性相关的通量缺陷的拓扑性质。我们开发了该框架的互补代数和场论表述，后者还暗示了向有隙拓扑有序相的自然过渡。此外，通过部分子构造，我们给出了玻色子系统中具有非阿贝尔涡旋的TOSF实例。
英文摘要
Topologically ordered superfluids (TOSFs) support deconfined, gapped anyonic excitations while remaining gapless because of Goldstone modes. We develop a general framework for characterizing their topological data in $(2+1)$-dimensional bosonic systems with spontaneously broken charge ${\rm U}(1)_{\rm c}$ symmetry. Gauging ${\rm U}(1)_{\rm c}$ maps a TOSF to a gapped topological order enriched by a dual ${\rm U}(1)_{\rm dual}$ symmetry with vanishing Hall conductance, while gauging ${\rm U}(1)_{\rm dual}$ recovers the TOSF. This two-way mapping allows the topological data of the TOSF, including the condensate charge, deconfined anyon content, and topological properties of vortices, to be systematically encoded using the algebraic framework of symmetry-enriched topological orders. In particular, superfluid vortices share the topological properties of flux defects associated with the residual discrete symmetry in the gapped anyon sector. We develop complementary algebraic and field-theoretic formulations of this framework, with the latter also suggesting a natural transition to a gapped topologically ordered phase. Additionally, using parton constructions, we present examples of TOSFs with non-Abelian vortices in bosonic systems.
发表机构
- Cornell University（康奈尔大学）
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