Density-Matrix Renormalization Group studies of mixture of two different ultracold bosonic atoms

We investigate the ground state phase diagram for a two species Bose mixture in a one dimensional optical lattice using the finite size density matrix renormalization group (FSDMRG) method. We present our result for different combinations of inter and intra-species repulsion strengths with a commensurate filling factor. We obtain a superfluid (SF) to Mott insulator (MI) transition when the inter species interaction term is less than the intra-species interaction term. However, when the former is slightly greater than the latter we find that the two different species reside in spatially separate regions