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

Abstract

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.

The ground-state phase diagram of the two-dimensional Falicov-Kimball model

“…In the one-dimensional case, the central region V has been found to contain a very complex structure [9,10]. In addition to the checkerboard configuration, a wealth of other periodic configurations are ground states in certain regions of the diagram.…”

“…In addition to the checkerboard configuration, a wealth of other periodic configurations are ground states in certain regions of the diagram. In fact, it is believed that configurations of arbitrary period occur in domains arranged to form a fractal structure, and that the dependence of ion density on chemical potential is a devil's staircase [3,9,10,19]. If a similar structure occurs in the two-dimensional model, then, it must be confined to V.…”

“…Previous work on the Falicov-Kimball model has concentrated on the one-dimensional case, and there the phase diagram has been found to have a very rich structure [3,8,9,10]. In particular, in the limit of large values of U only domains of the so-called most homogeneous configurations of the ions appear in the phase diagram constructed in the grand canonical ensemble [9,11,12].…”

“…On the other hand, for small values of U, other periodic phases appear in the phase diagram as well as the most homogeneous configurations. If additionally the density of the ions is close to zero (or unity) then the formation of molecules containing two or more ions (or vacancies) is observed [9,10].…”

Model of charge and magnetic order formation in itinerant electron systems

“…1 Later on the FKM appeared to be suitable for studying some other phenomena as well, as, e.g., a tendency for charge-densitywave formation in interacting fermion systems. [2][3][4] Actually, in most of applications studied so far the spinless version of the model was explored. As far as we know, spin degrees of freedom were taken into account only in a few papers, [5][6][7][8][9][10][11] but in all of them the interactions between electrons were spin independent.…”