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  • Open Access

Symmetry-deformed toric codes and the quantum dimer model

Jiaxin Qiao, Yoshito Watanabe*, and Simon Trebst

  • *Contact author: watanabe@thp.uni-koeln.de
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Phys. Rev. Research 7, 043342 – Published 30 December, 2025

DOI: https://doi.org/10.1103/f8p8-b5gw

Abstract

Motivated by the recent introduction of a U(1)-symmetric toric code (TC) model, we investigate symmetry-based deformations of topological order by systematically deconstructing the Gauss-law-enforcing star terms of the TC Hamiltonian. This “term-dropping” protocol introduces global symmetries that go beyond the alternative framework of “ungauging” topological order in symmetry-deformed models and gives rise to models such as the U(1)TC or XYTC. These models inherit (emergent) subsystem symmetries (from the original 1-form symmetry of the TC) that can give rise to (subextensive) ground-state degeneracies, which can still be organized by the eigenvalues of Wilson loop operators. However, we demonstrate that these models do not support topological or fracton order (as has been conjectured in the literature) due to the loss of (emergent) gauge symmetry. An extreme deformation of the TC is the quantum dimer model (QDM), which we discuss along the family of symmetry-deformed models from the perspective of subsystem symmetries, sublattice modulation, and quantum order-by-disorder mechanisms resulting in rich phase diagrams. For the QDM, this allows us to identify an emergent SO(2) symmetry for what appears to be a gapless ground state (by numerical standards) that is unstable to the formation of a plaquette valence bond solid upon sublattice modulation.

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Phys. Rev. Research 7, 043342– Published 30 December, 2025
  • Received 27 June 2025
  • Accepted 8 December 2025
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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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