  We implement a multi-orbital cluster dynamical mean-field theory (DMFT), by
improving a sample-update algorithm in the continuous-time quantum Monte Carlo
method based on the interaction expansion. The proposed sampling scheme for the
spin-flip and pair-hopping interactions in the two-orbital systems mitigates
the sign problem, giving an efficient way to deal with these interactions. In
particular, in the single-site DMFT, we see that the negative signs vanish. We
apply the method to the two-dimensional two-orbital Hubbard model at half
filling, where we take into account the short-range spatial correlation effects
within a four-site cluster. We show that, compared to the single-site DMFT
results, the critical interaction value for the metal-insulator transition
decreases and that the effects of the spin-flip and pair-hopping terms are less
significant in the parameter region we have studied. The present method
provides a firm starting point for the study of inter-site correlations in
multi-orbital systems. It also has a wide applicable scope in terms of
realistic calculations in conjunction with density functional theory.
