Phase separation and metal-insulator transitions in the spin-one-half Falicov-Kimball model

The ground-state phase diagram of the spin-one-half Falicov-Kimball model (FKM) is studied in the one dimension using small-cluster exact-diagonalization calculations. The resultant exact solutions are used to examine possibilities for valence and metal-insulator transitions in this model. A number of remarkable results are found. (i) The phase separation in the spin-one-half FKM takes place for a wide range of $f$-electron concentrations $n_f$ and $d$-$f$ interactions $G$, including $G$ large. (ii) In the strong coupling limit ($G>4$) the model exhibits a pressure induced discontinuous insulator-metal transition from an integer-valence state ($n_f=1$) into another integer-valence state ($n_f=0$). (iii) For intermediate values of $G$ ($G\sim 2.5$) the FKM undergoes a few discontinuous intermediate-valence transitions. There are several discontinuous insulator-insulator transitions from $n_f=1$ to $n_f=1/2$ and a discontinuous insulator-metal transition from $n_f = 1/2$ to $n_f=0$. (iv) In the weak coupling limit ($G<2$) the model undergoes a few consecutive discontinuous and continuous intermediate-valence transitions as well as a discontinuous metal-insulator transition.