Two-dimensional spin-polarized fermion lattice gases

A model of spin-polarized fermions hopping on a two-dimensional lattice with a nearest-neighbor interaction V is studied. Random-phase-approximation calculations predict that the half-filled system undergoes a density-wave transition for positive values of V, an odd-angular-momentum pairing transition for small negative V, and a condensation-phase-separation transition for more negative values of V. The classical lattice-gas Ising limit matches onto the density-wave transition for V>0 and the condensation transition for V<0. A strong-coupling expansion in powers of the ratio of single-fermion transfer-matrix element t to the two-body interaction V provides the leading corrections to the Ising limit. In order to explore the intermediate-coupling regime, fermion Monte Carlo calculations were carried out and various Greens functions characterizing the quantum correlations evaluated. With use of finite-size scaling techniques, the density-wave and condensation phase boundaries were followed into the intermediate-coupling regime. At these transitions, measured quantities scaled well with the usual Ising indices. Unfortunately, the weak-coupling regime lies beyond the reach of these simulations, and we conclude that a method suitable for the weak-coupling regime is needed to complete the phase diagram.