Interplay of localisation and competing interaction channels: cascade of quantum phase transitions
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 Us 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, |Us| U0, manifest itself in singularities of effective exchange integrals. |Us| U0 implies a frustration when the interactions standing alone drive the system to different phases. Even at Us=0, there is typically a QPT induced by Us sign change. Vector cold atoms, Fermions or Bosons, on optical lattices are the state-of-the-art realization of our system where Us is tunable in situ.