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arXiv:2506.01915 · Physical Review Letters

Magnetic Correlations in the SU(3) Triangular-Lattice t − J Model at Finite Doping

Annika Böhler, Fabian Grusdt, Annabelle Bohrdt

Published Jun 17, 2026• 1 citation
arXivHTMLPDF

Abstract

Ultracold alkaline-earth atoms and molecules now enable experimental realizations of SU(N)-symmetric Fermi-Hubbard models, yet theoretical understanding of these systems, particularly at finite doping remains limited. Here we investigate the strong-coupling limit of the SU(3) symmetric Fermi-Hubbard model on the triangular lattice across the full doping range. Using a three-flavor extension of Gutzwiller-projected hidden fermion determinant states (G-HFDS), a neural network based variational ansatz, we analyze two- and three-point spin-spin and spin-spin-hole correlations of the SU(3) Cartan generators. We further study the structure of a pair of doped holes for large periodic systems, and compare our results to the paradigmatic SU(2) square lattice equivalent, finding strikingly similar magnetic correlations, non-s-wave pairing symmetry, and enhanced binding energies. Our results provide a foundation for future exploration of doped SU(N) Mott insulators, providing insights for both theoretical developments and quantum simulation experiments.

DOI
10.1103/x68w-lwvv

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Ultracold alkaline-earth atoms and molecules now enable experimental realizations of SU(N)-symmetric Fermi-Hubbard models, yet theoretical understanding of these systems, particularly at finite doping remains limited. Here we investigate the strong-coupling limit of the SU(3) symmetric Fermi-Hubbard model on the triangular lattice across the full doping range. Using a three-flavor extension of Gutzwiller-projected hidden fermion determinant states (G-HFDS), a neural network based variational ansatz, we analyze two- and three-point spin-spin and spin-spin-hole correlations of the SU(3) Cartan generators. We further study the structure of a pair of doped holes for large periodic systems, and compare our results to the paradigmatic SU(2) square lattice equivalent, finding strikingly similar magnetic correlations, non-s-wave pairing symmetry, and enhanced binding energies. Our results provide a foundation for future exploration of doped SU(N) Mott insulators, providing insights for both theoretical developments and quantum simulation experiments.
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The physics of doped Mott insulators is at the heart of strongly correlated materials and is believed to constitute an essential ingredient for high-temperature superconductivity. In systems with higher SU(N)\mathrm{SU}(N)SU(N) spin symmetries, even richer magnetic ground states appear at a filling of one particle per site compared to the case of SU(2)\mathrm{SU}(2)SU(2) spins, but their fate upon doping remains largely unexplored. Here we address this question by studying a single hole in the SU(3) $t\text{\ensuremath{-}}J$ model whose undoped ground state features long-range, diagonal spin stripes. By analyzing both ground-state and dynamical properties utilizing the density matrix renormalization group, we establish the appearence of magnetic polarons consisting of chargons and flavor defects whose dynamics is constrained to a single effective dimension along the ordered diagonal. We semi-analytically describe the system using geometric string theory, where paths of hole motion are the fundamental degrees of freedom. With recent advances in the realization and control of SU(N)\mathrm{SU}(N)SU(N) Fermi-Hubbard models with ultracold atoms in optical lattices, our results can directly be observed in quantum gas microscopes with single-site resolution. Our work suggests the appearance of intricate ground states at finite doping constituted by emergent, coupled Luttinger liquids along diagonals, and is a first step towards exploring a wealth of physics in doped SU(N)\mathrm{SU}(N)SU(N) Fermi-Hubbard models on various geometries.
Sub-dimensional magnetic polarons in the one-hole doped SU(3) ttt-JJJ model
The physics of doped Mott insulators is at the heart of strongly correlated materials and is believed to constitute an essential ingredient for high-temperature superconductivity. In systems with higher SU(N) spin symmetries, even richer magnetic ground states appear at a filling of one particle per site compared to the case of SU(2) spins, but their fate upon doping remains largely unexplored. Here we address this question by studying a single hole in the SU(3) ttt-JJJ model, whose undoped ground state features long-range, diagonal spin stripes. By analyzing both ground state and dynamical properties utilizing the density matrix renormalization group, we establish the appearence of magnetic polarons consisting of chargons and flavor defects, whose dynamics is constrained to a single effective dimension along the ordered diagonal. We semi-analytically describe the system using geometric string theory, where paths of hole motion are the fundamental degrees of freedom. With recent advances in the realization and control of SU(N) Fermi-Hubbard models with ultracold atoms in optical lattices, our results can directly be observed in quantum gas microscopes with single-site resolution. Our work suggests the appearance of intricate ground states at finite doping constituted by emergent, coupled Luttinger liquids along diagonals, and is a first step towards exploring a wealth of physics in doped SU(N) Fermi-Hubbard models on various geometries.
We develop a self-consistent variant of the constrained path quantum Monte Carlo approach which ensures its independence of the trial wave function, and apply the method to compute ground-state correlations in the two-dimensional SU(3) Fermi-Hubbard Hamiltonian at 13\frac{1}{3}31​ filling, modeling fermions with three possible spin flavors moving on a square lattice with an average of one particle per site. We provide clear evidence of a quantum critical point separating a nonmagnetic uniform metallic phase from a regime where long-range ``spin'' order is present. This discovery of multiple successive transitions to magnetic states with regular, long-range alternation of the different flavors, whose symmetry changes as the interaction strength increases, significantly extends previous work in the Heisenberg limit to itinerant fermions. In addition to the rich quantum magnetism, this important physical system allows one to study integer filling and the associated Mott transition disentangled from nesting, in contrast to the usual SU(2) model, while preserving the square-lattice geometry. Our results also provide a significant step towards the interpretation of present and future experiments on fermionic alkaline-earth atoms, and other realizations of SU(N)\mathrm{SU}(N)SU(N) physics.
We investigate the evolution of the Mott insulators in the triangular lattice Hubbard Model, as a function of hole doping $\ensuremath{\delta}$ in both the strong and intermediate coupling limits. Using the advanced density matrix renormalization group (DMRG) method, at light hole doping $\ensuremath{\delta}\ensuremath{\lesssim}10%$, we find a significant difference between strong and intermediate couplings. Notably, at intermediate coupling an unusual metallic state emerges, with short ranged spin correlations but long ranged spin-chirality order. Moreover, no clear Fermi surface or wave vector is observed, this chiral metal also exhibits staggered loop current, which breaks the translational symmetry. These features disappear on increasing interaction strength or on further doping. At strong coupling, the 120 degree magnetic order of the insulating magnet persists for light doping, and produces hole pockets with a well-defined Fermi surface. On further doping, $\ensuremath{\delta}\ensuremath{\approx}10%\ensuremath{\sim}20%$ SDW order and coherent hole Fermi pockets are found at both strong and intermediate couplings. At even higher doping $\ensuremath{\delta}\ensuremath{\gtrsim}20%$, the SDW order is suppressed and the spin-singlet Cooper pair correlations are simultaneously enhanced. We also briefly comment on the strong particle-hole asymmetry of the model.
Simulating large, strongly interacting fermionic systems remains a major challenge for existing numerical methods. In this Letter, we introduce Gutzwiller projected hidden fermion determinant states (G-HFDS) to simulate the strongly interacting limit of the Fermi-Hubbard model, namely the t-J model, across the entire doping regime. We demonstrate that the G-HFDS achieve energies competitive with matrix product states on lattices as large as 10×10 sites while using several orders of magnitude fewer parameters, suggesting the potential for efficient application to even larger system sizes. This remarkable efficiency enables us to probe low-energy physics across the full doping range, providing new insights into the competition between kinetic and magnetic interactions and the nature of emergent quasiparticles. Starting from the low-doping regime, where magnetic polarons dominate the low energy physics, we track their evolution with increasing doping and different next-nearest neighbor hopping amplitudes through analyses of spin and polaron correlation functions as well as the Fermi surface. Our findings demonstrate the potential of determinant-based neural quantum states with an inherent fermionic sign structure, opening the way for simulating large-scale fermionic systems at any particle filling.