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 f-electron concentration [Formula: see text] on the f-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 p). (iii) At finite [Formula: see text] the main valence structure is formed by plateaus located at [Formula: see text], where i runs over the smallest integers. Strong effects of the orbital magnetic field are also observed on the formation and condensation of d-f 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] for small and intermediate values of f-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 d-f interaction, which leads to completely different ground state phase diagrams of the model for [Formula: see text] and [Formula: see text].