The ground-state phase diagram of the spinless 1D falicov-kimball model: Numerical studies

Extrapolation of small-cluster exact-diagonalization calculations is used to study the ground state phase diagram of the spinless one-dimensional Falicov-Kimball model at half filling. Our results show that the phase diagram has an extremely simple structure for the Coulomb interactionsU≥2. Here the ground states are the most homogeneous configurations (mhc) with the smallest periods. Valence transitions are discontinuous and only of the type insulator-insulator. In this region the finite size effects are negligible and thus the picture of valence transitions is definitive. ForU<2 the phase diagram exhibits a more complicated structure. Here we have specified a domain where the ground states are the mhc and a metallic domain where the ground states are mixtures of configurations with the empty configuration. The boundary between these two domains is the boundary of discontinuous insulator-metal transitions. Unlike the caseU≥2 the valence transitions are gradual in the weak coupling limit. This work was supported by the Slovak scientific grant agency VEGA, contract No. 4177/97.