Topological $Z_4$ spin-orbital liquid on the honeycomb lattice
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866917240584011776 |
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| author | Yamada, Masahiko G. |
| author_facet | Yamada, Masahiko G. |
| contents | We perform large-scale density matrix renormalization group simulations of the $\mathrm{SU}(4)$ Heisenberg model on the honeycomb lattice and resolve the long-standing question of its ground state in an unbiased and quantitatively controlled manner. We find compelling numerical evidence that the ground state is a gapped $Z_4$ spin-orbital liquid, characterized by a finite topological entanglement entropy close to $\ln(4)$, the absence of both $\mathrm{SU}(4)$ and lattice symmetry breaking, and a variationally optimized ground-state energy well below competing Dirac spin liquid states. By exploiting full $\mathrm{SU}(4)$ symmetry and keeping up to 12,800 $\mathrm{SU}(4)$ multiplets, corresponding to more than one million $\mathrm{U}(1)$ states, we achieve unprecedented accuracy for two-dimensional $\mathrm{SU}(4)$ quantum magnets. Finite-size scaling of energies and entanglement entropies supports a robust gapped phase in the two-dimensional limit, while a gapless critical state on narrow cylinders is identified as a proximate remnant of a Dirac spin-orbital liquid. Our results establish the $\mathrm{SU}(4)$ honeycomb Heisenberg model as a concrete realization of a gapped $Z_4$ spin-orbital liquid and provide robust numerical evidence for topological order in a highly symmetric two-dimensional quantum magnet. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_06549 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Topological $Z_4$ spin-orbital liquid on the honeycomb lattice Yamada, Masahiko G. Strongly Correlated Electrons We perform large-scale density matrix renormalization group simulations of the $\mathrm{SU}(4)$ Heisenberg model on the honeycomb lattice and resolve the long-standing question of its ground state in an unbiased and quantitatively controlled manner. We find compelling numerical evidence that the ground state is a gapped $Z_4$ spin-orbital liquid, characterized by a finite topological entanglement entropy close to $\ln(4)$, the absence of both $\mathrm{SU}(4)$ and lattice symmetry breaking, and a variationally optimized ground-state energy well below competing Dirac spin liquid states. By exploiting full $\mathrm{SU}(4)$ symmetry and keeping up to 12,800 $\mathrm{SU}(4)$ multiplets, corresponding to more than one million $\mathrm{U}(1)$ states, we achieve unprecedented accuracy for two-dimensional $\mathrm{SU}(4)$ quantum magnets. Finite-size scaling of energies and entanglement entropies supports a robust gapped phase in the two-dimensional limit, while a gapless critical state on narrow cylinders is identified as a proximate remnant of a Dirac spin-orbital liquid. Our results establish the $\mathrm{SU}(4)$ honeycomb Heisenberg model as a concrete realization of a gapped $Z_4$ spin-orbital liquid and provide robust numerical evidence for topological order in a highly symmetric two-dimensional quantum magnet. |
| title | Topological $Z_4$ spin-orbital liquid on the honeycomb lattice |
| topic | Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2601.06549 |