«Anticommuting» $\mathbb{Z}_2$ quantum spin liquids

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Hauptverfasser: Pujari, Sumiran, Nigam, Harsh
Format: Preprint
Veröffentlicht: 2025
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author Pujari, Sumiran
Nigam, Harsh
author_facet Pujari, Sumiran
Nigam, Harsh
contents We discuss a class of lattice $S=\frac{1}{2}$ quantum Hamiltonians with bond-dependent Ising couplings and a mutually «anticommuting» algebra of extensively many local $\mathbb{Z}_2$ conserved charges that was explicated in [arXiv:2407.06236]. This mutual algebra is reminiscent of the spin-$\frac{1}{2}$ Pauli matrix algebra but encoded in the structure of \emph{local conserved charges}. These models have finite residual entropy density in the ground state with a simple but non-trivial degeneracy counting and concomitant quantum spin liquidity as proved in [arXiv:2407.06236]. The spin liquidity relies on a geometrically site-interlinked character of the local conserved $\mathbb{Z}_2$ charges that is rather natural in presence of an «anticommuting» structure, as opposed to for example the bond-interlinked character of the local conserved $\mathbb{Z}_2$ hexagonal plaquette charges of the Kitaev honeycomb spin-$\frac{1}{2}$ model which leads to a mutually commuting local algebra. In this work, we make several exact statements on the many-body order that can be present within the class of «anticommuting» quantum spin liquids. We elucidate the differences between the many-body order in these models and that found in some gapped quantum spin liquids with mutually commuting local algebras, e.g. the Kitaev toric code or Levin-Wen models. We also point out a mutually commuting algebra with local support that are naturally expressed as multi-linear Majorana forms in the Kitaev representation of these quantum spin liquids. They capture non-trivial quantum resonances throughout the lattice in these «anticommuting» $\mathbb{Z}_2$ quantum spin liquid Hamiltonians.
format Preprint
id arxiv_https___arxiv_org_abs_2506_03866
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle «Anticommuting» $\mathbb{Z}_2$ quantum spin liquids
Pujari, Sumiran
Nigam, Harsh
Strongly Correlated Electrons
Statistical Mechanics
We discuss a class of lattice $S=\frac{1}{2}$ quantum Hamiltonians with bond-dependent Ising couplings and a mutually «anticommuting» algebra of extensively many local $\mathbb{Z}_2$ conserved charges that was explicated in [arXiv:2407.06236]. This mutual algebra is reminiscent of the spin-$\frac{1}{2}$ Pauli matrix algebra but encoded in the structure of \emph{local conserved charges}. These models have finite residual entropy density in the ground state with a simple but non-trivial degeneracy counting and concomitant quantum spin liquidity as proved in [arXiv:2407.06236]. The spin liquidity relies on a geometrically site-interlinked character of the local conserved $\mathbb{Z}_2$ charges that is rather natural in presence of an «anticommuting» structure, as opposed to for example the bond-interlinked character of the local conserved $\mathbb{Z}_2$ hexagonal plaquette charges of the Kitaev honeycomb spin-$\frac{1}{2}$ model which leads to a mutually commuting local algebra. In this work, we make several exact statements on the many-body order that can be present within the class of «anticommuting» quantum spin liquids. We elucidate the differences between the many-body order in these models and that found in some gapped quantum spin liquids with mutually commuting local algebras, e.g. the Kitaev toric code or Levin-Wen models. We also point out a mutually commuting algebra with local support that are naturally expressed as multi-linear Majorana forms in the Kitaev representation of these quantum spin liquids. They capture non-trivial quantum resonances throughout the lattice in these «anticommuting» $\mathbb{Z}_2$ quantum spin liquid Hamiltonians.
title «Anticommuting» $\mathbb{Z}_2$ quantum spin liquids
topic Strongly Correlated Electrons
Statistical Mechanics
url https://arxiv.org/abs/2506.03866