In this paper, we investigate the ground-state properties of a mixture of two species of fermionic atoms in a one-dimensional optical lattice, as described by the asymmetric Hubbard model. The quantum phase transition from density wave to phase separation is investigated by studying both the corresponding charge order parameter and quantum entanglement. A rigorous proof that even for the single-hole doping case, the density wave is unstable to the phase separation in the infinite
U limit, is given. Therefore, our results are quite instructive for both ongoing experiments on strongly correlated cold-atomic systems and traditional heavy fermion systems.
In this paper, we study the role of both "spin"(species) and mass imbalance in a mixture of two species of fermionic atoms with attractive interaction in an one-dimensional optical lattice. Using the bosonization approach, quantum phase transitions between a liquid phase and phase separated states are studied under various conditions of interaction, spin imbalance, and mass imbalance. We find that, in the phase-separated region, there exists two kinds of phase separation and a special quantum phase transition might exist between them in the large
U limit. On the other hand, the singlet superconducting correlation dominates in the liquid phase. The pairing behavior has been also demonstrated that there is oscillating behavior in real space. We find both the spin and mass imbalance are in favor of the formation of Fulde-Ferrell-Larkin-Ovchinnikov state.