Vanishing Hall conductance for all finite-range frustration-free models

Prove that the Hall conductance vanishes for every finite-range frustration-free model.

Background

The paper proves vanishing Hall conductance for translation-invariant free Fermion frustration-free ground states, while explaining that the broader statement is motivated by the known result for frustration-free commuting Hamiltonians.

The authors formulate the general claim as a natural conjecture and explicitly state that they do not know how to prove it in general. Their analysis therefore addresses only the translation-invariant free-fermion case rather than resolving the conjecture for arbitrary finite-range frustration-free models.

References

It is a natural conjecture that, in fact, the Hall conductance in any finite range frustration-free model is zero. We do not know how to prove this conjecture in general and we focus on the case of free Fermion models.

— Free Fermion frustration-free models have zero Hall conductance  (2610.21172 - Bachmann et al., 15 Oct 2026) in Section 1, Introduction