A Constructive Approach to Topological Invariants for One-dimensional Strictly Local Operators
Mathematical Physics
2021-09-21 v1 math.MP
Abstract
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.
Cite
@article{arxiv.2010.14466,
title = {A Constructive Approach to Topological Invariants for One-dimensional Strictly Local Operators},
author = {Yohei Tanaka},
journal= {arXiv preprint arXiv:2010.14466},
year = {2021}
}