The spectral localizer for semifinite spectral triples-Reference-Cited by-同舟云学术

The spectral localizer for semifinite spectral triples

Published:2020-10-20 Issue:1 Volume:149 Page:121-134
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Schulz-Baldes Hermann,Stoiber Tom

Abstract

The notion of a spectral localizer is extended to pairings with semifinite spectral triples. By a spectral flow argument, any semifinite index pairing is shown to be equal to the signature of the spectral localizer. As an application, a formula for the weak invariants of topological insulators is derived. This provides a new approach to their numerical evaluation.

Funder

Studienstiftung des Deutschen Volkes

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

https://www.ams.org/proc/2021-149-01/S0002-9939-2020-15230-6/proc15230_AM.pdf

Reference22 articles.

1. An analytic approach to spectral flow in von Neumann algebras;Benameur, Moulay-Tahar,2006

2. Non-commutative Chern numbers for generic aperiodic discrete systems;Bourne, Chris;J. Phys. A,2018

3. Application of semifinite index theory to weak topological phases;Bourne, Chris,2018

4. Fredholm theories in von Neumann algebras. I;Breuer, Manfred;Math. Ann.,1968

5. Spectral flow for nonunital spectral triples;Carey, A. L.;Canad. J. Math.,2015

Cited by 12 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Interacting local topological markers: A one-particle density matrix approach for characterizing the topology of interacting and disordered states;Physical Review Research;2024-08-28

2. Approximations of Interface Topological Invariants;SIAM Journal on Mathematical Analysis;2024-08-05

3. Topological zero-modes of the spectral localizer of trivial metals;Physical Review B;2024-05-01

4. Local Markers for Crystalline Topology;Physical Review Letters;2024-02-16

5. Topological Indices in Condensed Matter;Reference Module in Materials Science and Materials Engineering;2024