The two-state, one-dimensional, spinless Fermi gas (Falicov-Kimball model) is studied exactly by numerical calculation and perturbation theory. Rigorous results are presented for small interaction strength and (restricted) coherent and incoherent phase diagrams are calculated for two specific examples. The numerical calculations are extrapolated to provide a qualitative picture of the complete solution. The result includes a fractal structure in which the ground-state changes discontinuously as a function of the parameters.

• Received 24 July 1989

DOI:https://doi.org/10.1103/PhysRevB.41.2163