Edge Spectrum for Truncated \(\mathbb {Z}_2\)-Insulators

IF 1.1 3区数学 Q3 MATHEMATICS, APPLIED

Mathematical Physics, Analysis and Geometry Pub Date : 2025-08-23 DOI:10.1007/s11040-025-09520-4

Alexis Drouot, Jacob Shapiro, Xiaowen Zhu

引用次数: 0

Abstract

Fermionic time-reversal-invariant insulators in two dimension – class AII in the Kitaev table – come in two different topological phases. These are characterized by a \(\mathbb {Z}_2\)-invariant: the Fu–Kane–Mele index. We prove that if two such insulators with different indices occupy regions containing arbitrarily large balls, then the spectrum of the resulting operator fills the bulk spectral gap. Our argument follows a proof by contradiction developed in [16] for quantum Hall systems. It boils down to showing that the \(\mathbb {Z}_2\)-index can be computed only from bulk information in sufficiently large balls. This is achieved via a result of independent interest: a local trace formula for the \(\mathbb {Z}_2\)-index.

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截断\(\mathbb {Z}_2\)绝缘子的边缘谱

二维费米子时逆不变绝缘子（基塔耶夫表中的AII类）有两种不同的拓扑相。它们的特征是\(\mathbb {Z}_2\)不变量：Fu-Kane-Mele指数。我们证明了如果两个不同指标的绝缘子占据了包含任意大球的区域，则得到的算子的频谱填充了整体频谱间隙。我们的论证遵循了[16]中关于量子霍尔系统的矛盾证明。它可以归结为表明\(\mathbb {Z}_2\) -索引只能从足够大的球中的批量信息中计算。这是通过独立感兴趣的结果实现的：\(\mathbb {Z}_2\) -指数的本地跟踪公式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematical Physics, Analysis and Geometry 数学-物理：数学物理

CiteScore

2.10

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： MPAG is a peer-reviewed journal organized in sections. Each section is editorially independent and provides a high forum for research articles in the respective areas. The entire editorial board commits itself to combine the requirements of an accurate and fast refereeing process. The section on Probability and Statistical Physics focuses on probabilistic models and spatial stochastic processes arising in statistical physics. Examples include: interacting particle systems, non-equilibrium statistical mechanics, integrable probability, random graphs and percolation, critical phenomena and conformal theories. Applications of probability theory and statistical physics to other areas of mathematics, such as analysis (stochastic pde''s), random geometry, combinatorial aspects are also addressed. The section on Quantum Theory publishes research papers on developments in geometry, probability and analysis that are relevant to quantum theory. Topics that are covered in this section include: classical and algebraic quantum field theories, deformation and geometric quantisation, index theory, Lie algebras and Hopf algebras, non-commutative geometry, spectral theory for quantum systems, disordered quantum systems (Anderson localization, quantum diffusion), many-body quantum physics with applications to condensed matter theory, partial differential equations emerging from quantum theory, quantum lattice systems, topological phases of matter, equilibrium and non-equilibrium quantum statistical mechanics, multiscale analysis, rigorous renormalisation group.