Theory of oblique topological insulators
Theory of oblique topological insulators
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DOI：
10.21468/scipostphys.14.2.023
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发表时间：
2022-06
期刊：
影响因子：
5.5
通讯作者：
Benjamin Moy;Hart Goldman;R. Sohal;E. Fradkin
中科院分区：
文献类型：
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作者：
Benjamin Moy;Hart Goldman;R. Sohal;E. Fradkin
在物质拓扑相的研究中，一个长期存在的问题是理解在3+1维中可能存在的分数级拓扑绝缘体(FTI)相的类型。与普通的自由费米子拓扑绝缘体不同，FTI相具有分数Θ角、长程纠缠和分级化等特点。从Cardy和Rabinovici提出的一族简单的ℤN格点规范理论出发，基于斜禁闭的物理机制和广义整体对称性的现代语言，我们发展了一类FTI相。我们称这些相为斜拓扑绝缘体。当电荷的双子束束态和单极子凝聚时，就会产生倾斜，导致FTI相具有拓扑有序，出现一种形式的对称性，以及仅在2+1维中不能实现的带隙边界态。在格点规范理论的基础上，我们提出了含有起伏的一形式和二形式规范场的倾斜TI相的连续统拓扑量子场理论。我们明确地证明了这些TQFT同时捕获了在格点规范理论中看到的广义整体对称性和拓扑序。我们还证明了当存在两种形式的背景规范场时，这些理论表现出普遍的“广义磁电效应”。此外，我们刻画了斜TIS的可能的边界拓扑序，找到了以前没有研究过的一组新的边界状态。
A long-standing problem in the study of topological phases of matter has been to understand the types of fractional topological insulator (FTI) phases possible in 3+1 dimensions. Unlike ordinary topological insulators of free fermions, FTI phases are characterized by fractional \ThetaΘ-angles, long-range entanglement, and fractionalization. Starting from a simple family of \mathbb{Z}_NℤN lattice gauge theories due to Cardy and Rabinovici, we develop a class of FTI phases based on the physical mechanism of oblique confinement and the modern language of generalized global symmetries. We dub these phases oblique topological insulators. Oblique TIs arise when dyons—bound states of electric charges and monopoles—condense, leading to FTI phases characterized by topological order, emergent one-form symmetries, and gapped boundary states not realizable in 2+1-D alone. Based on the lattice gauge theory, we present continuum topological quantum field theories (TQFTs) for oblique TI phases involving fluctuating one-form and two-form gauge fields. We show explicitly that these TQFTs capture both the generalized global symmetries and topological orders seen in the lattice gauge theory. We also demonstrate that these theories exhibit a universal “generalized magnetoelectric effect” in the presence of two-form background gauge fields. Moreover, we characterize the possible boundary topological orders of oblique TIs, finding a new set of boundary states not studied previously for these kinds of TQFTs.