“…This condition is likely to be met in a variety of physical situations, as microscopic candidates are ubiquitous in complex materials -including soft lattice vibrations [5], critical modes in proximity of phase transitions [11], fluctuating magnetic moments [37], or collective charge fluctuations [33,38,39]. Regarding the latter, while charge fluctuations induced by the long-range Coulomb interactions between electrons may provide the slow bosonic modes enabling the appearance of a DDP [10,38,39], while short range correlations alone do not seem to sustain a DDP feature in the optical absorption [7][8][9]. On general grounds, local repulsive interactions are expected to suppress charge fluctuations and other forms of self-generated randomness, in particular at integer fillings.…”