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Global Structure of the Falicov-Kimball Model Ground State Phase Diagram

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Lach J., Łyżwa R., Jędrzejewski J.

Acta Physica Polonica A

1993

vol. 84

issue 2

327-344

The two-state spinless Falicov-Kimball model on a one-dimensional lattice is studied by means of well-controlled numerical 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 ρ_{e},ρ_{i} satisfy the conditions: ρ_{e} + ρ_{i} = 1, |ρ_{i} - 1/2| ≤ δ < 1/2. For all other pairs (ρ_{e},ρ_{i}) there is a critical U at which the system undergoes a conductor-insulator transition.

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1 Acta Physica Polonica A

1 1993

1 Jędrzejewski J.

1 Lach J.

1 Łyżwa R.

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Global Structure of the Falicov-Kimball Model Ground State Phase Diagram