The ground-state phase diagram of the spinless 1D Falicov-Kimball model: Numerical studies

Extrapolation of small-cluster exact-diagonalization calculations is used t o study the ground state phase diagram of the spinless one-dimensional Fali cov-Kimball model at half filling. Our results show that the phase diagram has an extremely simple structure for the Coulomb interactions U greater th an or equal to 2. Here the ground states are the most homogeneous configura tions (mhc) with the smallest periods. Valence transitions are discontinuou s and only of the type insulator-insulator. In this region the finite size effects are negligible and thus the picture of valence transitions is defin itive. For U < 2 the phase diagram exhibits a more complicated structure. H ere we have specified a domain where the ground states are the mhc and a me tallic domain where the ground states are mixtures of configurations with t he empty configuration. The boundary between these two domains is the bound ary of discontinuous insulator-metal transitions. Unlike the case U greater than or equal to 2 the valence transitions are gradual in the weak couplin g limit.