The topology of mobility-gapped insulators

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Abstract

Studying deterministic operators, we define a topology on the space of mobility-gapped insulators such that topological invariants are continuous maps into discrete spaces, we prove that this is indeed the case for the integer quantum Hall effect, and lastly we show why our “insulator” condition makes sense from the point of view of the localization theory using the fractional moments method.

Original languageEnglish (US)
Pages (from-to)2703-2723
Number of pages21
JournalLetters in Mathematical Physics
Volume110
Issue number10
DOIs
StatePublished - Oct 1 2020
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Keywords

  • Integer quantum Hall effect
  • Mobility gap
  • Random Schrödinger operators
  • Strong disorder
  • Topological insulators

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