The influence of f-electron hopping on ground states and valence transitions in the extended Falicov-Kimball model

Abstract

The ground-state phase diagram of the extended Falicov-Kimball model with f-f electron hopping is studied numerically in the one-dimensional case. To identify the nature of ground states three complementary numerical methods are used, and namely, (i) the small-cluster exact-diagonalization method, (ii) the density-matrix-renormalization-group method (DMRG) and (iii) an approximate, but very accurate, numerical method based on the reduction of the Hilbert space. It is found that the physics of the Falicov-Kimball model found for the zero value of the f-electron hopping integral tf (including the existence of the devil’s staircase structure) persists also at finite values of tf. The critical values of tcf below which the physics of the Falicov-Kimball model dominates are calculated numerically and it is shown that they depend very strongly on the f-electron concentration nf and only very weakly on the Coulomb interaction. In particular, we have found that for strong Coulomb interactions the value of tcf rapidly increases from tcf ~ 0.003 found for nf = 1 / 4 up to relatively large tcf ~ 0.4 found for nf near the half-filled band case nf = 1 / 2. In addition, the complete picture of valence transitions is presented for non-zero tf and strong Coulomb interactions.