Spectral localization for semimetals and Callias operators

2022/03/28 by Hermann Schulz‐Baldes, Schulz-Baldes, Hermann, Tom Stoiber +1 · 3 citations
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics #Topological Materials and Phenomena

paper · pdf · doi:10.48550/arxiv.2203.15014

openalex publication_date 2022/03/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A semiclassical argument is used to show that the low-lying spectrum of a selfadjoint operator, the so-called spectral localizer, determines the number of Dirac or Weyl points of an ideal semimetal. Apart from the IMS localization procedure, an explicit computation for the local toy models given by a Dirac or Weyl point is the key element of proof. The argument has numerous similarities to Witten's reasoning leading to the strong Morse inequalities. The same techniques allow to prove a spectral localization for the Callias operator in terms of a multi-parameter spectral flow of selfadjoint Fredholm operators.

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