On the BCS-BEC Crossover in the 2D Asymmetric Attractive Hubbard Model

We analyze the evolution from the weak coupling (BCS-like limit) to the strong coupling limit of tightly bound local pairs in the 2D asymmetric attractive Hubbard model, in the presence of the Zeeman magnetic field (h). The broken symmetry Hartree approximation is used. We also apply the Kosterlitz-Thouless scenario to determine the phase coherence temperatures. We obtain that for the spin dependent hopping integrals $(t^{↑} ≠ t^{↓})$ the homogeneous polarized superfluid $(SC_{M})$ phase in the ground state for the strong attraction and lower filling can be stabilized. We find a topological quantum phase transition (the Lifshitz type) from the unpolarized superfluid phase $(SC_0)$ to $SC_{M}$ and tricritical point in the (h - μ) and spin polarization (P) vs. attraction (U < 0) ground state phase diagrams. The finite temperatures phase diagrams for $t^{↑} ≠ t^{↓}$ are constructed.