手性和粒子空穴对称拓扑链的Z2不变量

IF 0.5 4区 数学 Q3 MATHEMATICS Journal of Mathematical Physics Analysis Geometry Pub Date : 2023-03-15 DOI:10.1063/5.0138647
Domenico Monaco, Gabriele Peluso
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引用次数: 0

摘要

我们定义了与任意满足粒子-空穴对称或手性对称的一维平移不变拓扑绝缘子相关的z2值拓扑和规范不变量。不变量可以从与合适的Bloch函数基相关联的Berry相位计算,该基与对称性兼容。我们计算了手性对称绝缘子的Su-Schrieffer-Heeger模型和粒子-空穴对称绝缘子的Kitaev模型中的不变量。我们证明了在这两种情况下,Z2不变量预测了相应截断模型的零能量边界态的存在。
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A Z2 invariant for chiral and particle–hole symmetric topological chains
We define a Z2-valued topological and gauge invariant associated with any one-dimensional, translation-invariant topological insulator that satisfies either particle–hole symmetry or chiral symmetry. The invariant can be computed from the Berry phase associated with a suitable basis of Bloch functions that is compatible with the symmetries. We compute the invariant in the Su–Schrieffer–Heeger model for chiral symmetric insulators and in the Kitaev model for particle–hole symmetric insulators. We show that in both cases, the Z2 invariant predicts the existence of zero-energy boundary states for the corresponding truncated models.
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来源期刊
CiteScore
0.70
自引率
20.00%
发文量
18
审稿时长
>12 weeks
期刊介绍: Journal of Mathematical Physics, Analysis, Geometry (JMPAG) publishes original papers and reviews on the main subjects: mathematical problems of modern physics; complex analysis and its applications; asymptotic problems of differential equations; spectral theory including inverse problems and their applications; geometry in large and differential geometry; functional analysis, theory of representations, and operator algebras including ergodic theory. The Journal aims at a broad readership of actively involved in scientific research and/or teaching at all levels scientists.
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