Mott transitions in ternary flavor mixtures of ultracold fermions on optical lattices

Ternary flavor mixtures of ultracold fermionic atoms in an optical lattice are studied in the case of equal repulsive on-site interactions $U>0$. The corresponding SU(3) invariant Hubbard model is solved numerically exactly within dynamical mean-field theory using multigrid Hirsch-Fye quantum Monte Carlo simulations. We establish Mott transitions close to integer filling at low temperatures and show that the associated signatures in the compressibility and pair occupancy persist to high temperatures, i.e., they should be accessible to experiments. In addition, we present spectral functions and discuss the properties of a “semicompressible” state observed for large $U$ near half filling.

Figure 1

(Color online) HF-QMC estimates of particle density $n\left(\mu \right)$ at $T=t^{\ast }/20$ for various on-site interactions $U$. Plateaus at integer filling indicate localized Mott phases (for $U/t^{\ast }\ge 6$). In the inset, curves are shifted (in steps of 0.1) for clarity.

Figure 2

(Color online) HF-QMC estimates of pair occupancy $D$ at $T=t^{\ast }/20$ vs chemical potential $\mu$ (main panel) and vs density $n$ (inset), respectively. The suppression of $D$ with increasing $U$ is clearly enhanced on the Mott plateau at $n\approx 1$.

Figure 3

(Color online) HF-QMC estimates of compressibility $\kappa =dn/d\mu$ at $T=t^{\ast }/20$ as a function of chemical potential $\mu$ (main panel) and density $n$ (inset), respectively.

Figure 4

(Color online) Multigrid HF-QMC estimates of density $n\left(\mu \right)$ (top panel) and compressibility $\kappa \left(\mu \right)=dn\left(\mu \right)/d\mu$ (bottom panel) at interaction $U/t^{\ast }=6$ for various temperatures $T$. The strong suppression of $\kappa$ at $n\approx 1$ survives up to $T\approx t^{\ast }/5⪢T^{\ast }\approx t^{\ast }/20$. For comparison, thin solid lines indicate HF-QMC data for $T=t^{\ast }/20$ (cf. Figs. 1, 3).

Figure 5

(Color online) Multigrid HF-QMC estimates of spectral function $A\left(\omega \right)$ for $T=t^{\ast }/10$, $U/t^{\ast }=6$ at different values of $\mu$, corresponding to densities $n=1.5$, 1.27, 1.07, 1.00, 0.9996, and 0.91 (from top to bottom).