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Anticommuting Z2 quantum spin liquids

Sumiran Pujari1,2,* and Harsh Nigam3

  • *Contact author: sumiran.pujari@iitb.ac.in
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Phys. Rev. B 113, 064402 – Published 2 February, 2026

DOI: https://doi.org/10.1103/dhh4-8wkj

Abstract

We discuss a class of lattice S=12 quantum Hamiltonians with bond-dependent Ising couplings and a mutually “anticommuting” algebra of extensively many local Z2 conserved charges that was explicated by Pujari [arXiv:2407.06236]. This mutual algebra is reminiscent of the spin-12 Pauli matrix algebra but encoded in the structure of local conserved charges. These models have finite residual entropy density in the ground state with a simple but nontrivial degeneracy counting and concomitant quantum spin liquidity as proved by Pujari [arXiv:2407.06236]. The spin liquidity relies on a geometrically site-interlinked character of the local conserved Z2 charges that is rather natural in the presence of an anticommuting structure. One may contrast this with, for example, the bond-interlinked character of the local conserved Z2 charges on the hexagonal plaquettes of the Kitaev honeycomb spin-12 model, which leads to a mutually commuting local algebra. In this work, we make several exact statements on the kinds of many-body orders that can be present within the class of anticommuting quantum spin liquids coexisting with extensive residual ground state entropy. We elucidate the differences between the many-body order in these models and that found in some gapped quantum spin liquids whose canonical example is the Kitaev toric code. The toric code belongs to the more general class of Levin-Wen or string net constructions that possess mutually commuting algebras for the local conserved charges. We also point out a mutually commuting algebra with local support that is naturally expressed as multilinear Majorana forms in the Kitaev representation of these quantum spin liquids. They capture quantum resonances spread across the lattice in anticommuting Z2 quantum spin liquids.

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Phys. Rev. B 113, 064402– Published 2 February, 2026
  • Received 18 July 2025
  • Revised 27 October 2025
  • Accepted 26 November 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. Open access publication funded by Max Planck Society.

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