Spectral Flow of Monopole Insertion in Topological Insulators

Carey AL, Schulz-Baldes H (2019)

Publication Type: Journal article

Publication year: 2019

Journal

Communications in Mathematical Physics Springer Verlag (Germany)

Book Volume: 370

Pages Range: 895-923

Journal Issue: 3

DOI: 10.1007/s00220-019-03310-0

Abstract

Inserting a magnetic flux into a two-dimensional one-particle Hamiltonian leads to a spectral flow through a given gap which is equal to the Chern number of the associated Fermi projection. This paper establishes a generalization to higher even dimension by inserting non-abelian monopoles of the Wu-Yang type. The associated spectral flow is then equal to a higher Chern number. For the study of odd spacial dimensions, a new so-called ‘chirality flow’ is introduced which, for the insertion of a monopole, is then linked to higher winding numbers. This latter fact follows from a new index theorem for the spectral flow between two unitaries which are conjugates of each other by a self-adjoint unitary.

Authors with CRIS profile

Hermann Schulz-Baldes Professur für Mathematik (Mathematische Physik)

Involved external institutions

Australian National University (ANU) AU Australia (AU)

How to cite

APA:

Carey, A.L., & Schulz-Baldes, H. (2019). Spectral Flow of Monopole Insertion in Topological Insulators. Communications in Mathematical Physics, 370(3), 895-923. https://dx.doi.org/10.1007/s00220-019-03310-0

MLA:

Carey, Alan L., and Hermann Schulz-Baldes. "Spectral Flow of Monopole Insertion in Topological Insulators." Communications in Mathematical Physics 370.3 (2019): 895-923.

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