Fractionalization, emergent SU($N$) symmetries, and fragmentation in layered quantum spin-orbital models
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866910247393689600 |
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| author | Cônsoli, Pedro M. Vijayvargia, Aayush Erten, Onur |
| author_facet | Cônsoli, Pedro M. Vijayvargia, Aayush Erten, Onur |
| contents | We propose a family of layered quantum spin-orbital models as a platform to study fractionalization, unconventional forms of symmetry-breaking order, and their possible coexistence. The models are built by stacking $N$ layers of a square-lattice system in which Kitaev-type interactions promote the formation of a $\mathbb{Z}_2$ quantum spin-orbital liquid and coupling the different layers via Ising spin interactions. Using a parton construction, we show how, at low energies, these Hamiltonians can be mapped to $N$-component Fermi Hubbard models on a $π$-flux square lattice at half filling. We also demonstrate that the models acquire an emergent SU($N$) symmetry in the limit of equal all-to-all interlayer couplings and argue that, for $N>2$, the proximity to this limit offers the potential to realize an array of competing phases. To illustrate this point, we compute the zero-temperature phase diagram of the effective $N=3$ Hubbard model within mean-field theory and uncover rich phenomena, including intertwined orders and flavor-selective localization. Mapping back to the original degrees of freedom reveals that the ground states realize distinct forms of magnetic fragmentation, wherein the orbitals remain in a quantum liquid state whereas the spins can present conventional long-range order or nonlocal order characterized by a nontrivial string order parameters. We highlight possible extensions of our construction as well as its potential to provide concrete microscopic models for different fractionalized quantum critical points. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_22908 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Fractionalization, emergent SU($N$) symmetries, and fragmentation in layered quantum spin-orbital models Cônsoli, Pedro M. Vijayvargia, Aayush Erten, Onur Strongly Correlated Electrons We propose a family of layered quantum spin-orbital models as a platform to study fractionalization, unconventional forms of symmetry-breaking order, and their possible coexistence. The models are built by stacking $N$ layers of a square-lattice system in which Kitaev-type interactions promote the formation of a $\mathbb{Z}_2$ quantum spin-orbital liquid and coupling the different layers via Ising spin interactions. Using a parton construction, we show how, at low energies, these Hamiltonians can be mapped to $N$-component Fermi Hubbard models on a $π$-flux square lattice at half filling. We also demonstrate that the models acquire an emergent SU($N$) symmetry in the limit of equal all-to-all interlayer couplings and argue that, for $N>2$, the proximity to this limit offers the potential to realize an array of competing phases. To illustrate this point, we compute the zero-temperature phase diagram of the effective $N=3$ Hubbard model within mean-field theory and uncover rich phenomena, including intertwined orders and flavor-selective localization. Mapping back to the original degrees of freedom reveals that the ground states realize distinct forms of magnetic fragmentation, wherein the orbitals remain in a quantum liquid state whereas the spins can present conventional long-range order or nonlocal order characterized by a nontrivial string order parameters. We highlight possible extensions of our construction as well as its potential to provide concrete microscopic models for different fractionalized quantum critical points. |
| title | Fractionalization, emergent SU($N$) symmetries, and fragmentation in layered quantum spin-orbital models |
| topic | Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2605.22908 |