Ferromagnetic ground state of SU(3) Hubbard model on the Lieb lattice

Abstract

We investigate the magnetic properties of a repulsive fermionic SU($3$) Hubbard model on the Lieb lattice from weak to strong interaction by means of the mean-field approximation. To validate the method we employed, we first discuss the SU($2$) Hubbard model at the mean-field level, and find that our results are consistent with known rigorous theorems. We then extend the calculation to the case of SU($3$) symmetry. We find that, at $4/9$ filling, the SU$(3)$ symmetry spontaneously breaks into the SU$(2)\times$U$(1)$ symmetry in the ground state, leading to a staggered ferromagnetic state for any repulsive $U$ at zero temperature. We then investigate the stability of the ferromagnetic state by relaxing the filling away from $4/9$, and conclude that the ferromagnetic state is sensitive but robust to fillings, as it can persist within a certain filling regime. We also apply the mean-field approximation to finite temperature to calculate the critical temperature and the critical entropy of the ferromagnetic state. As the resulting critical entropy per particle is significantly greater than that can be realized in experiments, we expect some quasi-long-range-ordered features of such a ferromagnetic state can be realized and observed with fermionic alkaline-earth-metal(-like) atoms loaded into optical lattices.

11 pages, 10 figures

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Cited by in corpus (13)

• Universal thermodynamics of an SU($N$) Fermi-Hubbard Model
• Metal-insulator transition and magnetism of SU(3) fermions in the square lattice
• Metal-insulator transition and quantum magnetism in the SU(3) Fermi-Hubbard Model: Disentangling Nesting and the Mott Transition
• Analytical Solution for the Steady States of the Driven Hubbard model
• Many-body Physics of Ultracold Alkaline-Earth atoms with SU($N$)-symmetric interactions
• Flat-band Ferromagnetism of the SU$(N)$ Hubbard Model on the Tasaki Lattice
• Relation between the noise correlations and the spin structure factor for Mott-insulating states in SU$(N)$ Hubbard models
• A generalized effective spin-chain formalism for strongly interacting spinor gases in optical lattice
• Altermagnetism and its induced higher-order topology on the Lieb lattice
• Flat band effects on the ground-state BCS-BEC crossover in atomic Fermi gases in a quasi-two-dimensional Lieb lattice
• Partial suppression of magnetism in the square lattice SU(3) Hubbard model
• Itinerant ferromagnetism in an SU(3) Fermi-Hubbard model at finite temperatures: A dynamical mean-field theory study
• Defect-induced edge ferromagnetism and fractional spin excitations of the SU(4) $\pi$-flux Hubbard model on honeycomb lattice