Minimal energy ensemble Monte Carlo for the partition function of fermions coupled to classical fields

Models of non-interacting fermions coupled to auxilliary classical degrees of freedom are relevant to the understanding of a wide variety of problems in many body physics, {\it e.g.} the description of manganites, diluted magnetic semiconductors or strongly interacting electrons on lattices. Monte Carlo sampling over the classical fields is a powerful, yet notoriously challenging, method for this class of problems -- it requires the solution of the fermion problem for each classical field configuration. Conventional Monte Carlo methods minimally utilize the information content of these solutions by extracting single temperature properties. We present a flat-histogram Monte Carlo algorithm that simulates a novel statistical ensemble which allows to acquire the full thermodynamic information, {\it i.e.} the partition function at all temperatures, of sampled classical configurations.