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.
We propose that a combination of the semiclassical approximation with Monte Carlo simulations can be an efficient and reliable impurity solver for dynamical mean field theory equations and their cluster extensions with large cluster sizes. In order to show the reliability of the method, we consider two test cases: (i) the single-band Hubbard model within the dynamical cluster approximation with four- and eight-site clusters and (ii) the anisotropic two-orbital Hubbard model with orbitals of different bandwidth within the single-site dynamical mean field theory. We compare the critical interaction
Uc/t with those obtained from solving the dynamical mean field equations with the continuous-time and Hirsch-Fye quantum Monte Carlo approaches. In both test cases we observe reasonable values of the metal-insulator critical interaction strength
Uc/t and the nature of Mott physics in the self-energy behavior. While some details of the spectral functions cannot be captured by the semiclassical approximation due to the freezing of dynamical fluctuations, the main features are reproduced by the approach.