The role of hybridization on valence transitions in the spinless Falicov-Kimball model

The spinless Falicov-Kimball model with hybridization is studied in one dimension using small-cluster exact-diagonalization calculations. The resultant exact solutions are used to examine the f-state occupation n ^f as a function of f-level energy E _f, hybridization V and d-f interaction U. In addition, the phase diagram based on the finite-size scaling analysis of the single particle excitation energy is discussed both for the symmetric (E _f = 0) and unsymmetric (E _f ≠ 0) case. A number of remarkable results are found. (i) The f-electron occupation number as a function of E _f changes continuously, confirming renormalization-group results. No discontinuous transitions are observed at finite V. (ii) In the symmetric case the insulating state persists as the ground state for all nonzero V. (iii) Outside the symmetric point the hybridization stabilizes the metallic state for lower V and the insulating state for higher V. (iv) The metal-insulator transition takes place at V = V _c > 0. The values of the critical hybridization strength V _c are of order 10^?2.