Vanishing Hall conductance for commuting Hamiltonians

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.

5 pages, 2 figures. Supplemental material added

References in corpus (1)

• Local stabilizer codes in three dimensions without string logical operators

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