Dynamical Cluster Approximation Study of the Anisotropic Two-Orbital Hubbard Model

We investigate the properties of a two-orbital Hubbard model with unequal bandwidths on the square lattice in the framework of the dynamical cluster approximation (DCA) combined with a continuous-time quantum Monte Carlo algorithm. We explore the effect of short-range spatial fluctuations on the nature of the metal-insulator transition and the possible occurrence of an orbital-selective Mott transition (OSMT) as a function of cluster size $N_c$. We observe that for $N_c=2$ no OSMT is present, instead a band insulator state for both orbitals is stabilized at low temperatures due to the appearance of an artificial local ordered state. For $N_c=4$ the DCA calculations suggest the presence of five different phases which originate out of the cooperation and competition between spatial fluctuations and orbitals of different bandwidths and an OSMT phase is stabilized. Based on our results, we discuss the nature of the gap opening.

Figure 1

(a) On site and intersite interorbital spin-spin correlations for $N_c=2$ as a function of $U/t$ at temperatures $T/t=0.1$ and $T/t=0.3$. (b) Double occupancy for $N_c=2$ as a function of $T/t$ for $U/t=2.4$. Left and right axes are for the double occupancy of the narrow band and the wide band, respectively.

Figure 2

(a) The on site (intersite) interorbital spin-spin correlations for $N_c=2$ and 4 as a function of $U/t$ at $T/t=0.1$. (b) The narrow band (next) nearest-neighbor spin-spin (NNN, NN) correlations for $N_c=2$ and 4 as a function of $U/t$ at $T/t=0.1$.

Figure 3

The imaginary part of the on site self-energy for $U/t=1.0$, 1.4, 2.2, 3.0, 3.4 at $T/t=0.1$ for $N_c=4$ (a) in the narrow band and (b) in the wide band. The real (c) and imaginary (d) part of self-energy at the lowest Matsubara frequency ${\omega }_0$ for $K=(\pi ,\pi )$ and ($\pi$, 0) sectors as a function of $U/t$.

Figure 4

Density of states at $T/t=0.1$ and $N_c=4$ for (a) $U/t=2.8$ and (b) $U/t=3.4$. We employ the Padé approximation method for the analytic continuation.

Figure 5

The phase diagram with five phases for $N_c=4$.