On the phases of the 1D asymmetric Hubbard model with balanced species

An asymmetric variant of the fermionic Hubbard model, with different hopping coefficients for the two species, was originally introduced to model certain metal-insulator transitions in solid-state physics and has recently gathered a renewed interest in the context of optical lattices. Here we discuss a series of numerical results for the one-dimensional case with equally populated species, obtained by means of the density-matrix renormalisation group. We consider both the repulsive case, where phase separation may occur, and the attractive case to study the robustness of pairing correlations with increasing asymmetry. We also inspect the nature of the excitations related to population imbalance (the "spin gap"). These results are compared to bosonisation predictions and to perturbative calculations in the strong and weak coupling regimes.