Modulated phases in the Falicov-Kimball model

The arrangement of localized f electrons in the ground state of the Falicov-Kimball model is studied as a function of the energy of the f-level. For the half-filled case in one dimension, perturbation theory in the d-electron bandwidth together with numerical results reveals a sequence of transitions between long-period modulated arrangements of the f electrons. Results suggest the existence of a multiphase point at zero d-band-width and f energy, and a complete devil's staircase for the variation of f occupation as the energy of the f-level is changed when the d-bandwidth is nonzero.