Ground-state properties of the asymmetric Hubbard model are studied on one-dimensional clusters (rings) with N = 6, 6, and 10 sites. The ground-state energy, correlation functions, and phase diagrams are determined for various sets of model parameters. Computations are performed both by exact diagonalization (for N = 6) and by an approximate method by which correlation efiect's can be examined on larger clusters than exact diagonalization allows. In the limiting cases (one limit corresponds to the spinless Falicov-Kimball model and the other to the Hubbard model) our results agree quite well with those obtained analytically for in6nite systems.

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The two-state spinless Falicov-Kimball model on a one-dimensional lattice is studied by means of well-controlled numericał procedures. Restricted phase diagrams in the grand-canonical ensemble and at zero temperature are constructed. The evolution of these phase diagrams, as the interaction parameter U is varied, including the band structures corresponding to configurations of localized particles (ions) and densities of mobile particles (electrons), is monitored. The changes observed enable us to draw conclusions for the global structure of the phase diagram and to make a qualitative plot of such a diagram. Particular attention is paid to the possibility of conductor-insulator transitions. The results obtained suggest that the system is an insulator for all U only if the electron and ion densities pc, p; satisfy the conditions: pe+ pi =1, 'pi -1/2|< δ < 4. For all other pairs (Pc , pi) there is a critical U at which the system undergoes a conductor-insulator transition.