Few-body bound states of bosonic mixtures in two-dimensional optical lattices

We study the formation of bound states in a binary mixture of a few bosons in square optical lattices. Using the exact diagonalization method, we find that bound clusters of all available bosons can form. We provide a comprehensive numerical examination of these bound states for a wide range of repulsive intraspecies and attractive interspecies interactions. In contrast to binary mixtures in one-dimensional chains, we reveal that the binding energy of the clusters shows a non-monotonic dependence on the interspecies interaction strengths for small tunneling rates, developing a local minimum for intermediate attractive interactions. The findings of this work highlight the difference between the binding mechanisms of binary bosonic mixtures in one- and higher-dimensional lattices.