Fractionalization, emergent SU(N) symmetries, and fragmentation in layered quantum spin-orbital models
Abstract
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 ℤ2 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.
Versions
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BibTeX
@misc{consoli2026fractionalization,
title = {{Fractionalization, emergent SU($N$) symmetries, and fragmentation in layered quantum spin-orbital models}},
author = {Pedro M. Cônsoli and Aayush Vijayvargia and Onur Erten},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2605.22908},
eprint = {2605.22908},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.22908},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Fractionalization, emergent SU(N) symmetries, and fragmentation in layered quantum spin-orbital models
AU - Pedro M. Cônsoli
AU - Aayush Vijayvargia
AU - Onur Erten
PY - 2026
DA - 2026/08/27
PB - arXiv
DO - 10.48550/arxiv.2605.22908
UR - https://arxiv.org/abs/2605.22908
AB - 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 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.
ER -