Generalized Nagaoka ferromagnetism accompanied by flavor-selective Mott states in an SU($N$) Fermi-Hubbard model

TL;DR

This work investigates ferromagnetism in SU($N$) Fermi-Hubbard models on a hypercubic lattice using DMFT combined with continuous-time QMC. It shows that in the strong-coupling, low-temperature regime, FM states appear away from commensurate fillings, with SU($3$) exhibiting a flavor-selective Mott state coexisting with FM near one-third filling, and SU($4$) hosting six distinct FM types as density varies. The results reveal two complementary mechanisms for FM at commensurate fillings: generalized Nagaoka ferromagnetism with $N-1$ localized flavors and one itinerant, and flavor-selective Mott ferromagnetism where $N-1$ flavors are localized; the total number of FM states scales as $2(N-1)$. The study highlights the rich magnetic behavior enabled by SU($N$) symmetry and provides experimentally accessible predictions for ultracold-atom systems, while noting the importance of lattice geometry for FM stability.

Abstract

We study the ferromagnetic instability in an SU($N$) Fermi-Hubbard model on the hypercubic lattice. Combining dynamical mean-field theory with continuous-time quantum Monte Carlo simulations, we find that, in the strong-coupling regime at low temperatures, ferromagnetically ordered (FM) states develop away from the commensurate fillings. In the particle-doped SU($3$) system near one-third filling, the FM state is accompanied by a spontaneous flavor-selective Mott state, where two of the three flavors are Mott insulating while the remaining flavor is metallic. Since particles in the metallic flavor can almost freely move on the lattice without correlation effects, the ordered state is stabilized by the kinetic-energy gain of the doped particles. This is similar to the generalized Nagaoka ferromagnetism discussed in the one-hole-doped system at one-third filling. In the SU($4$) case, we find that six distinct types of FM states appear as the particle density varies. The results uncover the nature of the FM state in the SU($N$) Fermi-Hubbard systems and highlight the rich magnetic behavior enabled by enlarged internal symmetries.

Figures (8)

• Figure 1: (a) Total number of particles $n_{\mathrm{tot}}$ as a function of the chemical potential for the $\mathrm{SU}(3)$ Fermi-Hubbard model at $T/D = 0.01$ when $U/D = 3$ (blue), $30$ (green), and $300$ (magenta). The dashed line indicates the chemical potential corresponding to the half-filled condition. (b) Magnetic susceptibility as a function of $n_{\mathrm{tot}}$ for $U/D = 300$ when $T/D=0.010$ (blue), $0.012$ (green), and $0.016$ (magenta).
• Figure 2: (a) Particle density $n_\sigma$, (b) double occupancy $d_{\sigma,\sigma'}$, and (c) the quantity $A_\sigma$ in the $\mathrm{SU}(3)$ Fermi--Hubbard model with $U/D = 300$ and $n_{\mathrm{tot}} = 1.02$. The red dashed line in (c) represents the value of the noninteracting DOS corresponding to $n_3 = 0.02$.
• Figure 3: Magnetization $m$ (right axis) and inverse magnetic susceptibility $1/\chi D$ (left axis) as functions of the interaction strength $U/D$ for the $\mathrm{SU}(3)$ Fermi-Hubbard model at $T/D = 0.003$ and $n_{\mathrm{tot}} = 1.02$.
• Figure 4: Finite-temperature phase diagram of the $\mathrm{SU}(3)$ Fermi-Hubbard model for $U/D = 300$ around one-third filling $(n_{\mathrm{tot}}\sim 1)$. Blue (red) circles and crosses represent the phase transition points, where FM-I (FM-II) and PM states disappear, respectively. The Mott insulating state at one-third filling $n_{\mathrm{tot}}=1$ is indicated by the dashed line. The flavor occupancies for FM-I, FM-II, and Mott states are illustrated.
• Figure 5: (a) Overall behavior of the susceptibility as a function of $n_{\mathrm{tot}}$ in the $\mathrm{SU}(4)$ Fermi-Hubbard model for $U/D = 300$ when $T/D = 0.01, 0.012$, and $0.016$. (b) [(c)] Enlarged views of the regions around $n_{\mathrm{tot}}=1$ ($n_{\mathrm{tot}}=2$).