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

TL;DR

This paper introduces a flat-histogram Monte Carlo algorithm that efficiently computes the partition function across all temperatures for fermion models coupled to classical fields, improving over traditional methods.

Contribution

The paper presents a novel flat-histogram Monte Carlo method that captures the full thermodynamic information of fermion-classical field systems in a single simulation.

Findings

Efficiently computes partition functions at all temperatures.

Reduces computational cost compared to traditional methods.

Provides comprehensive thermodynamic data from a single simulation.

Abstract

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.