The K-Theoretic Bulk-Edge Correspondence for Topological Insulators

被引：36
|
作者：
Bourne, Chris [1 ,2 ,3 ,4 ]
Kellendonk, Johannes [5 ]
Rennie, Adam [3 ]
机构：
[1] Tohoku Univ, Adv Inst Mat Res, Aoba Ku, 2-1-1 Katahira, Sendai, Miyagi 9808577, Japan
[2] Australian Natl Univ, Math Sci Inst, Canberra, ACT 0200, Australia
[3] Univ Wollongong, Sch Math & Appl Stat, Wollongong, NSW 2522, Australia
[4] Friedrich Alexander Univ Erlangen Nurnberg, Dept Math, Cauerstr 11, D-91058 Erlangen, Germany
[5] Univ Claude Bernard Lyon 1, Inst Camille Jordan, CNRS UMR 5208, F-69622 Villeurbanne, France
来源：
ANNALES HENRI POINCARE | 2017年 / 18卷 / 05期
基金：
澳大利亚研究理事会;
关键词：
LOCAL INDEX FORMULA; NONCOMMUTATIVE GEOMETRY; CROSSED-PRODUCTS; ALGEBRAS I; QUANTIZATION; CURRENTS; STATES;
D O I：
10.1007/s00023-016-0541-2
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
We study the application of Kasparov theory to topological insulator systems and the bulk-edge correspondence. We consider observable algebras as modelled by crossed products, where bulk and edge systems may be linked by a short exact sequence. We construct unbounded Kasparov modules encoding the dynamics of the crossed product. We then link bulk and edge Kasparov modules using the Kasparov product. Because of the anti-linear symmetries that occur in topological insulator models, real -algebras and KKO-theory must be used.
引用
收藏
页码：1833 / 1866
页数：34
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