Mott transitions of three-component fermionic atoms with repulsive interaction in optical lattices

We investigate the Mott transitions of three-component (colors) repulsive fermionic atoms in optical lattices using the dynamical mean-field theory. We find that for SU(3) symmetry-breaking interactions, the Mott transition occurs at incommensurate half filling. As a result, a characteristic Mott insulating state appears, where paired atoms with two different colors and atoms with the third color are localized, and either of these states is randomly distributed in each site. We also find another Mott state, where atoms with two different colors are randomly localized at different sites, and atoms with the third color remain itinerant. We demonstrate that double occupancy measurements show characteristics of these exotic Mott phases.

Figure 1

Quasiparticle weight $Z_{\alpha }$ and double occupancy $D_{\alpha \beta }$ (a) for $U^{″}/U=1.5$ and $U^{\prime }/U=0.7$ as a function of $U/t$, and (b) for $U^{″}/U=1.5$ and $U/t=8.0$ as a function of $U^{\prime }/U$.

Figure 2

For $U\ne U^{\prime }=U^{″}$, quasiparticle weight $Z_{\alpha }$ and double occupancy $D_{\alpha \beta }$ for (a) $U^{\prime }/U=0.5$ and (b) $U^{\prime }/U=1.5$ as a function of $U/t$. Since $U^{\prime }=U^{″}$, we obtain $Z_1=Z_2$ and $D_{13}=D_{23}$.

Figure 3

Phase diagrams of the three-component repulsive fermionic atoms in optical lattices at half filling for (a) $U^{″}/U=1.5$, (b) $U^{″}/U=1.0$, and (c) $U^{″}/U=0.5$. (d) Quasiparticle weight for $U=U^{\prime }=U^{″}$ as a function of the atom number $N$ per site. Because of the isotropic interaction, $Z\equiv Z_1=Z_2=Z_3$.

Figure 4

Quasiparticle weights (a) $Z_1$ for $U^{″}/U=0.5$ as a function of $\mathrm{Ũ}/t=|U^{″}-U|/t$ for $U^{\prime }/U=1.4,1.6,1.8$, and $2.0$, and (b) $Z_2$ for $U^{″}/U=1.5$ as a function of $\mathrm{Ũ}/t=|U^{\prime }-U|/t$ for $U^{\prime }/U=0.6,\hspace{0.5em}0.8,\hspace{0.5em}1.1$, and $1.3$.