论文标题
一维当地运营商的拓扑不变性的建设性方法
A Constructive Approach to Topological Invariants for One-dimensional Strictly Local Operators
论文作者
论文摘要
在本文中，我们将重点关注一维的严格本地运营商，其概念自然出现在离散时间量子行走的背景下，在一维整数晶格上。特别是，我们为与此类运营商相关的以下两个拓扑不变式提供了一种基本的建设性方法：弗雷霍尔姆指数和基本频谱。作为一个直接应用，我们将明确计算并完全对这些拓扑不变的量为众所周知的量子步行模型进行分类。
In this paper we shall focus on one-dimensional strictly local operators, the notion of which naturally arises in the context of discrete-time quantum walks on the one-dimensional integer lattice. In particular, we give an elementary constructive approach to the following two topological invariants associated with such operators: Fredholm index and essential spectrum. As a direct application, we shall explicitly compute and fully classify these topological invariants for a well-known quantum walk model.
