The ground-state phase diagram of the asymmetric Hubbard model is studied in
one and two dimensions by a well-controlled numerical method. The method allows
to calculate directly the probabilities of particular phases in the approximate
ground-state and thus to specify the stability domains corresponding to phases
with the highest probabilities. Depending on the electron filling $n$ and the
magnitude of the asymmetry $t_f/t_d$ between the hopping integrals of $f$ and
$d$ electrons two different scenarios in formation of ground states are
observed. At low electron fillings ($n\leq 1/3$) the ground states are always
phase segregated in the limit of strong asymmetry ($t_d\gg t_f$). With
decreasing asymmetry the system undergoes a transition to the phase separated
state and then to the homogeneous state. For electron fillings $n>1/3 $ and
weak Coulomb interactions the ground state is homogeneous for all values of
asymmetry, while for intermediate and strong interactions the system exhibits
the same sequence of phase transitions as for $n$ small. Moreover, it is shown
that the segregated phase is significantly stabilized with increasing electron
filling, while the separated phases disappear gradually from the ground-state
phase diagrams.Comment: 10 pages, 5 figure
A new numerical method is used to study the ground-state properties of the spinless FalicovKimball model in one and two dimensions. The resultant solutions are used to examine the phase diagram of the model as well as possibilities for valence and metal-insulator transitions. In one dimension a comprehensive phase diagram of the model is presented. On the base of this phase diagram, the complete picture of valence and metal-insulator transitions is discussed. In two dimensions the structure of groundstate configurations is described for intermediate interactions between f and d electrons. In this region the phase separation and metal-insulator transitions are found at low f -electron concentrations. It is shown that valence transitions exhibit a staircase structure.
PACS. 75.10.Lp Band and itinerant models -71.27.+a Strongly correlated electron systems; heavy fermions -71.28.+d Narrow-band systems; intermediate-valence solids -71.30.+h Metal-insulator transitions and other electronic transitions
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