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Generalized Hall conductivities in local commuting projector models: Generalized symmetries and protected surface modes

Po-Shen Hsin1 and Ryohei Kobayashi2

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Phys. Rev. B 113, 075106 – Published 3 February, 2026

DOI: https://doi.org/10.1103/94bv-37h1

Abstract

Hall conductivities are important characterizations of phases of matter. It is known that nonzero Hall conductivities are difficult to realize in local commuting projector lattice models due to no-go theorems in (2+1)D. In this work we construct local commuting projector models in (2+1)D and (3+1)D with nonzero generalized Hall conductivities for ordinary and higher-form continuous symmetries on tensor product Hilbert space of finite local dimension. The model is given by a standard ZN toric code, but the symmetries do not admit expression in terms of on-site charge operators. The symmetry do not have local charges or currents on the lattice in the absence of boundaries, but there is still a notion of Hall conductivities that coincide with the continuum field theories. We construct protected gapless boundaries of the lattice models using modified Villain formalism. The generalized Hall conductivities are computed by surface currents as well as bulk flux insertion and many-body Chern number.

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Outline

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Phys. Rev. B 113, 075106– Published 3 February, 2026
  • Received 24 September 2025
  • Revised 27 November 2025
  • Accepted 13 January 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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