Magnetic ordering of three-component ultracold fermionic mixtures in optical lattices

We study finite-temperature magnetic phases of three-component mixtures of ultracold fermions with repulsive interactions in optical lattices with simple cubic or square geometry by means of dynamical mean-field theory (DMFT). We focus on the case of one particle per site (1/3 band filling) at moderate interaction strength, where we observe a sequence of thermal phase transitions into two- and three-sublattice ordered states by means of the unrestricted real-space generalization of DMFT. From our quantitative analysis we conclude that long-range ordering in three-component mixtures should be observable at comparable temperatures as in two-component mixtures.

Figure 1

Dependence of the filling per site on the chemical potential for an SU(3)-symmetric mixture in the cubic lattice at $U=10t$ and $T=0.5t$ (paramagnetic region). (Inset) Dependence of the chemical potential $\mu /U$ on the interaction strength $U/t$ at filling $n=1$ for different temperatures, which shows that the shift is proportional to $t/U$.

Figure 2

Sketch of two types of sublattice ordering (above) and the corresponding three types of magnetic phases (below) observed in our R-DMFT analysis at 1/3 band filling for a three-component fermionic mixture. The depicted main two-sublattice ordered states (right) can be understood in the following way: CDW2–“1” and “2” team up against “3”, CSAF–“3” is left out of AF correlations.

Figure 3

Transitions between sublattice orderings at finite temperature obtained by R-DMFT for a cubic lattice (${12}^3$ sites). Parameters are $U_{12}=U+{\Delta }_{12}$, $U_{13}=U_{23}=U-{\Delta }_{12}/2$, $U=12t$.

Figure 4

Real-space total density and spin density profiles obtained by DMFT in a cubic lattice for anisotropic interaction strengths. Parameters are $T=4t$, $V_i=0.04t{(r_i/a)}^2$, where $a$ is the lattice spacing; (a)–(b): $U_{12}=U_{13}=20t$, $U_{23}=40t$, ${\mu }_1=45t$, ${\mu }_2={\mu }_3=60t$; (c)–(d): $U_{12}=U_{13}=40t$, $U_{23}=20t$, ${\mu }_1=60t$, ${\mu }_2={\mu }_3=45t$.