arXiv 2004.051232020-04hep-thcond-mat.str-el

界面与Chern-Simons理论的扩展Hilbert空间

Interfaces and the extended Hilbert space of Chern-Simons theory

Jackson R. Fliss, Robert G. Leigh

备注：: 46 pages, many figures, 1 appendix; v2: fixed affiliations, minor revisions, added references
DOI：: 10.1007/JHEP07(2020)009

摘要：

$(2+1)$维拓扑相的低能有效场论为研究物质的基态纠缠提供了强有力的途径。在\cite{Fliss:2017wop}中，利用Abel Chern-Simons理论和一组拓扑边界条件（TBCs）研究了不同Abel拓扑相之间的纠缠.在本文中，我们将TBC的概念扩展到非阿贝尔的陈-西蒙斯理论，为一类跨越非阿贝尔拓扑相的带隙界面提供了一个有效的描述。这些边界条件为量子理论的扩展希尔伯特空间提供了一个定义关系，并允许在规范理论中直接计算纠缠。因为我们允许平凡的接口，这包括一个通用的建设扩展希尔伯特空间在任何（紧凑）陈-西蒙斯理论量化的黎曼曲面。此外，这提供了一个建设性的和原则性的定义为希尔伯特空间的有效基态的有间隙的物质相粘沿有间隙的界面。最后，我们描述了一个广义的手术概念，增加了一个强大的工具，从拓扑场论的缺口接口工具箱。

英文摘要：

The low energy effective field theories of $(2+1)$ dimensional topological phases of matter provide powerful avenues for investigating entanglement in their ground states. In \cite{Fliss:2017wop} the entanglement between distinct Abelian topological phases was investigated through Abelian Chern-Simons theories equipped with a set of topological boundary conditions (TBCs). In the present paper we extend the notion of a TBC to non-Abelian Chern-Simons theories, providing an effective description for a class of gapped interfaces across non-Abelian topological phases. These boundary conditions furnish a defining relation for the extended Hilbert space of the quantum theory and allow the calculation of entanglement directly in the gauge theory. Because we allow for trivial interfaces, this includes a generic construction of the extended Hilbert space in any (compact) Chern-Simons theory quantized on a Riemann surface. Additionally, this provides a constructive and principled definition for the Hilbert space of effective ground states of gapped phases of matter glued along gapped interfaces. Lastly, we describe a generalized notion of surgery, adding a powerful tool from topological field theory to the gapped interface toolbox.

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。

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英文摘要：

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