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We address the system with two species of vector bosons in an opticallattice. In addition to the the standard parameters characterizing such asystem, we are dealing here with the "degree of atomic nonidentity",manifesting itself in the difference of tunneling amplitudes and on-siteCoulomb interactions. We obtain a cascade of quantum phase transitionsoccurring with the increase in the degree of atomic nonidentity. In particular,we show that the phase diagram for strongly distinct atoms is qualitativelydifferent from that for (nearly) identical atoms considered earlier. Theresulting phase diagrams evolve from the images similar to the "J. Mir\'o-likepaintings" to "K. Malewicz-like" ones.

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