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  • Open Access

Interacting electronic topology of nonlocal crystals

Shu Hamanaka1,*, Martina O. Soldini2,†, Tsuneya Yoshida1,‡, and Titus Neupert2,§

  • *Contact author: hamanaka.shu.45p@st.kyoto-u.ac.jp
  • †Contact author: martina.soldini@physik.uzh.ch
  • ‡Contact author: yoshida.tsuneya.2z@kyoto-u.ac.jp
  • §Contact author: titus.neupert@physik.uzh.ch
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Phys. Rev. Research 8, 043012 – Published 5 October, 2026

DOI: https://doi.org/10.1103/x226-5mcz

Abstract

Nonlocal crystals are systems with translational symmetry but arbitrary-range couplings or interactions between degrees of freedom. We argue that such systems can realize symmetry-allowed but locality-forbidden ground-state symmetry eigenvalues. This is demonstrated by constructing an exactly solvable fermionic model in a one-dimensional translationally invariant setting in symmetry class AII with inversion symmetry, using a Hatsugai-Kohmoto-type model. The resulting unique gapped ground state exhibits the size-independent inversion eigenvalue −1, which is allowed from the fixed-size zero-dimensional viewpoint but forbidden in both noninteracting band insulators and local crystalline fermionic symmetry-protected topological phases. Our work establishes Hatsugai-Kohmoto-type nonlocality as a concrete route to realizing symmetry sectors that are inaccessible in such local phases.

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Phys. Rev. Research 8, 043012– Published 5 October, 2026
  • Received 20 June 2025
  • Revised 4 November 2025
  • Accepted 18 September 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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