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  • Letter

Vanishing Hall conductance for commuting Hamiltonians

Carolyn Zhang* and Michael Levin†

Sven Bachmann‡

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

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

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

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.

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Phys. Rev. B 105, L081103– Published 8 February, 2022
  • Received 6 August 2021
  • Revised 16 November 2021
  • Accepted 19 January 2022
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