Metal-insulator transition and quantum magnetism in the SU(3) Fermi-Hubbard Model: Disentangling Nesting and the Mott Transition

Abstract

We use state-of-the-art numerical techniques to compute ground state correlations in the two-dimensional SU(3) Fermi Hubbard model at $1/3$-filling, modeling fermions with three possible spin flavors moving on a square lattice with an average of one particle per site. We find clear evidence of a quantum critical point separating a non-magnetic uniform metallic phase from a regime where long-range `spin' order is present. In particular, there are multiple successive transitions to states with regular, long-range alternation of the different flavors, whose symmetry changes as the interaction strength increases. 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. 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($N$) physics.

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• Many-body Physics of Ultracold Alkaline-Earth atoms with SU($N$)-symmetric interactions
• Extended Hubbard model describing small multi-dot arrays in bilayer graphene
• Preempting Fermion Sign Problem: Unveiling Quantum Criticality through Nonequilibrium Dynamics in Imaginary Time
• Combinatorial summation of Feynman diagrams: Equation of state of the 2D SU(N) Hubbard model
• Structural complexity of snapshots of 2D Fermi-Hubbard systems
• Itinerant ferromagnetism in an SU(3) Fermi-Hubbard model at finite temperatures: A dynamical mean-field theory study
• Partial suppression of magnetism in the square lattice SU(3) Hubbard model
• Solving the SU($N$) Orbital Hatsugai-Kohmoto Model
• Unit-density SU(3) Fermi-Hubbard Model with Spin Flavor Imbalance
• Density Matrix Renormalization Group simulations of the SU(N) Fermi-Hubbard chain implementing the full SU(N) symmetry via Semi-Standard Young Tableaux and Unitary Group Subduction Coefficients
• Dominant Excitonic Superconductivity in a Three-component Hubbard Chain
• $\mathrm{SU}(3)$ Fermi-Hubbard gas with three-body losses: symmetries and dark states
• Magnetic correlations in the $SU(3)$ triangular-lattice $t$-$J$ model at finite doping
• Trion formation and ordering in the attractive SU(3) Fermi-Hubbard model
• Generalized Nagaoka ferromagnetism accompanied by flavor-selective Mott states in an SU($N$) Fermi-Hubbard model