单元矩阵的流动一维和三维实空间缠绕数

arXiv - PHYS - Chaotic Dynamics Pub Date : 2024-05-21 DOI:arxiv-2405.12537

F. Hamano, T. Fukui

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引用次数: 0

摘要

基塔耶夫（Kitaev）提出的流概念是实网格上缠绕数的一种明显拓扑形式。首先，我们在本文中表明，流对于没有平移不变性的系统的实际数值计算非常有用。其次，我们将其扩展到三维空间。也就是说，我们推导出了三维网格上的流动公式，当系统具有平移不变性时，它与传统的绕组数相对应。

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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Flow of unitary matrices: Real-space winding numbers in one and three dimensions

The notion of the flow introduced by Kitaev is a manifestly topological formulation of the winding number on a real lattice. First, we show in this paper that the flow is quite useful for practical numerical computations for systems without translational invariance. Second, we extend it to three dimensions. Namely, we derive a formula of the flow on a three-dimensional lattice, which corresponds to the conventional winding number when systems have translational invariance.

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arXiv - PHYS - Chaotic Dynamics

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