Quantum phase transitions and the degree of nonidentity in the system with two different species of vector bosons

We present new results for the system with two species of vector bosons in an optical lattice. In addition to the standard parameters characterizing such a system, we are dealing here with the ‘degree of atomic nonidentity’, manifesting itself in the difference of tunneling amplitudes and on-site Coulomb interactions. We obtain a cascade of quantum phase transitions occurring with the increase in the degree of atomic nonidentity. While in the system of nearly identical vector bosons only one phase transition between two phases occurs with the evolution of the interparticle interaction, atom nonidentity increases the number of possible phases to six and the resulting phase diagrams are so nontrivial that we can speculate about their evolution from the images similar to the ‘J Miró-like paintings’ to ‘K Malewicz-like’ ones.