An Index Theorem for Quarter-Plane Toeplitz Operators via Extended Symbols and Gapped Invariants Related to Corner States

被引：1

作者：

Hayashi, Shin ^{[1
,2
,3
]}

机构：

[1] Tohoku Univ, Adv Inst Mat Res, 2 1 1 Katahira, Aoba, Sendai 9808577, Japan

[2] Japan Sci & Technol Agcy, PRESTO, 4 1 8 Honcho, Kawauchi, Saitama 3320012, Japan

[3] Natl Inst Adv Ind Sci & Technol, Math Adv Mat Open Innovat Lab, 2 1 1 Katahira, Aoba, Sendai 9808577, Japan

来源：

COMMUNICATIONS IN MATHEMATICAL PHYSICS | 2023年 / 400卷 / 01期

关键词：

K-THEORY; ALGEBRAS;

D O I：

10.1007/s00220-022-04600-w

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

In this paper, we discuss index theory for Toeplitz operators on a discrete quarter-plane of two-variable rational matrix function symbols. By using Gohberg-Krein theory for matrix factorizations, we extend the symbols defined originally on a two-dimensional torus to some three-dimensional sphere and derive a formula to express their Fredholm indices through extended symbols. Variants for families of (self-adjoint) Fredholm quarter-plane Toeplitz operators and those preserving real structures are also included. For some bulk-edge gapped single-particle Hamiltonians of finite hopping range on a discrete lattice with a codimension-two right angle corner, topological invariants related to corner states are provided through extensions of bulk Hamiltonians.

引用

页码：429 / 462

页数：34