Abstract
We investigate the interplay of localization, interactions and (pseudo)spin degrees of freedom on quantum states of particles on the lattice. Our results show that breaking the paradigm density-density interaction U₀≫ (pseudo)spin-(pseudo)spin interaction U_s will drive the sequence of quantum phase transitions (QPT), where (pseudo)spin state and particle ordering, in case of several particle species, on the lattice are strongly changed. QPT driven by competing interactions, |U_s|∼ U₀, manifest itself in singularities of effective exchange integrals. |U_s|∼ U₀ implies a frustration when the interactions standing alone drive the system to different phases. Even at U_s=0, there is typically a QPT induced by U_s sign change. Vector cold atoms, Fermions or Bosons, on optical lattices are the state-of-the-art realization of our system where U_s is tunable \textit{in situ}.