Phase separation and metal-insulator transitions in the spin-12Falicov-Kimball model

Abstract

The ground-state phase diagram of the spin-$\frac{1}{2}$ Falicov-Kimball model (FKM) is studied in 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-$\frac{1}{2}$ FKM takes place for a wide range of f-electron concentrations ${n}_{f}$ and $d\ensuremath{-}f$ 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 $(G\ensuremath{\sim}2.5)$ 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.