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arXiv:2306.16464 · Physical Review Research

Metal-insulator transition and quantum magnetism in the SU(3) Fermi-Hubbard model

Chunhan Feng, Eduardo Ibarra-García-Padilla, Kaden R. A. Hazzard, Richard T. Scalettar, Shiwei Zhang, Ettore Vitali

Published Dec 20, 2023• 26 citations
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Abstract

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 $\frac{1}{3}$ 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 $\mathrm{SU}(N)$ physics.

DOI
10.1103/physrevresearch.5.043267

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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.
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The SU(N)\mathrm{SU}(N)SU(N) Hubbard model is a natural extension of the SU(2)\mathrm{SU}(2)SU(2) model. However, even the N=3N=3N=3 case remains poorly understood. We report a ground-state phase diagram of the square lattice SU(3)\mathrm{SU}(3)SU(3) Fermi-Hubbard model. Using a backflow Ansatz, we identify strong signatures of a Mott transition and a subsequent magnetic transition, and the suppression of a previously predicted magnetic phase. We study the hole-doped model, identifying a transition from magnetic to paramagnetic behavior in the strong-coupling regime. Our findings offer a different ground-state picture. More broadly, our work suggests a path to study general SU(N)\mathrm{SU}(N)SU(N) Hubbard models with arbitrary filling and geometry.
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