Phys. Rev. B 105, L081103 (2022) - Vanishing Hall conductance for commuting Hamiltonians

Letter

Vanishing Hall conductance for commuting Hamiltonians

Carolyn Zhang, Michael Levin, and Sven Bachmann

Phys. Rev. B 105, L081103 – Published 8 February 2022

Abstract

We consider the process of flux insertion for ground states of almost local commuting projector Hamiltonians in two spatial dimensions. In the case of finite-dimensional local Hilbert spaces, we prove that this process cannot pump any charge, and we conclude that the Hall conductance must vanish.

Received 6 August 2021
Revised 16 November 2021
Accepted 19 January 2022

DOI:https://doi.org/10.1103/PhysRevB.105.L081103

©2022 American Physical Society

Physics Subject Headings (PhySH)

Geometric & topological phases Hall effect

2-dimensional systems

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Carolyn Zhang ^* and Michael Levin ^†

Department of Physics, Kadanoff Center for Theoretical Physics, University of Chicago, Chicago, Illinois 60637, USA

Sven Bachmann ^‡

Department of Mathematics, The University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z2

^*cczhang@uchicago.edu
^†malevin@uchicago.edu
^‡sbach@math.ubc.ca

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Issue

Vol. 105, Iss. 8 — 15 February 2022

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