Free Fermion frustration-free models have zero Hall conductance

Sven Bachmann; Zhiqian Du; Martin Fraas

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arXiv · 2610.21172

Free Fermion frustration-free models have zero Hall conductance

Sven Bachmann·Zhiqian Du·Martin Fraas

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Abstract

We give a new proof that translation-invariant free Fermion frustration-free models have zero Hall conductance. Our proof is analytic in nature and it uses the bulk-edge correspondence. The central argument, which holds beyond the translation-invariant situation, is that in frustration-free models, edge modes cannot merge into the ground state band. We give an example of a gapped frustration-free model that is nonetheless gapless on the half-plane.

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Sven Bachmann, Zhiqian Du, Martin Fraas. 2026-10-15. Free Fermion frustration-free models have zero Hall conductance. https://arxiv.org/abs/2610.21172

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