Eur. Phys. J. B (2014) 87: 209
https://doi.org/10.1140/epjb/e2014-50275-1

Regular Article

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

Institute of Experimental Physics, Slovak Academy of Sciences, Watsonova 47, 04001 Košice, Slovakia

^a e-mail: farky@saske.sk

Received: 28 April 2014
Received in final form: 18 June 2014
Published online: 16 September 2014

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 t_f (including the existence of the devil’s staircase structure) persists also at finite values of t_f. The critical values of t^c_f 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 n_f and only very weakly on the Coulomb interaction. In particular, we have found that for strong Coulomb interactions the value of t^c_f rapidly increases from t^c_f ~ 0.003 found for n_f = 1 / 4 up to relatively large t^c_f ~ 0.4 found for n_f near the half-filled band case n_f = 1 / 2. In addition, the complete picture of valence transitions is presented for non-zero t_f and strong Coulomb interactions.