«Anticommuting» $\mathbb{Z}_2$ quantum spin liquids
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arXiv
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| Format: | Preprint |
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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 |