GLOBAL STRUCTURE OF THE FALICOV-KIMBALL MODEL GROUND-STATE PHASE-DIAGRAM

The two-state spinless Falicov-Kimball model on a one-dimensional latt ice is studied by means of well-controlled numerical procedures. Restr icted phase diagrams in the grand-canonical ensemble and at zero tempe rature are constructed. The evolution of these phase diagrams, as the interaction parameter U is varied, including the band structures corre sponding to configurations of localized particles (ions) and densities of mobile particles (electrons), is monitored. The changes observed e nable us to draw conclusions for the global structure of the phase dia gram and to make a qualitative plot of such a diagram. Particular atte ntion is paid to the possibility of conductor-insulator transitions. T he results obtained suggest that the system is an insulator for all U only if the electron and ion densities rho(c), rho(i) satisfy the cond itions: rho(e) + rho(i) = 1, \rho(i) - 1/2\ less-than-or-equal-to delt a < 1/2. For all other pairs (rho(c), rho(i)) there is a critical U at which the system undergoes a conductor-insulator transition.