A \({\mathbb {Z}}_{2}\)-Topological Index for Quasi-Free Fermions

IF 0.9 3区数学 Q3 MATHEMATICS, APPLIED

Mathematical Physics, Analysis and Geometry Pub Date : 2022-03-14 DOI:10.1007/s11040-022-09421-w

N. J. B. Aza, A. F. Reyes-Lega, L. A. M. Sequera

引用次数: 1

Abstract

We use infinite dimensional self-dual \(\mathrm {CAR}\) \(C^{*}\)-algebras to study a \({\mathbb {Z}}_{2}\)-index, which classifies free-fermion systems embedded on \({\mathbb {Z}}^{d}\) disordered lattices. Combes–Thomas estimates are pivotal to show that the \({\mathbb {Z}}_{2}\)-index is uniform with respect to the size of the system. We additionally deal with the set of ground states to completely describe the mathematical structure of the underlying system. Furthermore, the weak\(^{*}\)-topology of the set of linear functionals is used to analyze paths connecting different sets of ground states.

查看原文本刊更多论文

准自由费米子的\({\mathbb {Z}}_{2}\) -拓扑指数

利用无限维自对偶\(\mathrm {CAR}\)\(C^{*}\) -代数研究了一个\({\mathbb {Z}}_{2}\) -指标，该指标对嵌入在\({\mathbb {Z}}^{d}\)无序格上的自由费米子系统进行了分类。库姆斯-托马斯的估计对于表明\({\mathbb {Z}}_{2}\) -指数相对于系统的大小是一致的至关重要。我们还处理了一组基态，以完整地描述底层系统的数学结构。此外，利用线性泛函集的弱\(^{*}\) -拓扑来分析连接不同基态集的路径。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

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.