The influence of orbital magnetic field on valence transitions and ferroelectric correlations in the spinless Falicov-Kimball model

A combination of the classical and projector quantum Monte-Carlo method is used to examine the effects of an orbital magnetic field on valence transitions and ferroelectric correlations in the two-dimensional spinless Falicov-Kimball model. Our results reveal three major effects of the orbital magnetic field on valence transitions (dependence of Formula: see text-electron concentration Formula: see text on the Formula: see text-level position Formula: see text), namely, (i) The magnetic flux Formula: see text most significantly stabilizes the plateau at Formula: see text; (ii) For small and intermediate values of the magnetic flux Formula: see text (Formula: see text) there is a discontinuous valence transition from the intermediate valence phase with Formula: see text to an integer valence phase with Formula: see text induced by Formula: see text (an external pressure Formula: see text). (iii) At finite Formula: see text the main valence structure is formed by plateaus located at Formula: see text, where Formula: see text runs over the smallest integers. Strong effects of the orbital magnetic field are also observed on the formation and condensation of Formula: see text-Formula: see text excitons. In particular, it is found that the ferroelectric correlations in the magnetic-field-induced case (Formula: see text) are significantly enhanced compared to the case Formula: see text = 0 for small and intermediate values of Formula: see text-electron concentrations and that this effect is the most pronounced for Formula: see text, where the enhancement reaches the value Formula: see text for small and Formula: see text for intermediate values of Formula: see text-Formula: see text interaction, which leads to completely different ground state phase diagrams of the model for Formula: see text=0 and Formula: see text.