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

Area of Science:

• Condensed matter physics
• Statistical mechanics
• Computational physics

Background:

• Models of noninteracting fermions coupled to classical fields are crucial for understanding complex phenomena like manganites and strongly correlated electron systems.
• Existing methods may face challenges in efficiently acquiring complete thermodynamic information for such systems across all temperatures.

Purpose of the Study:

• To develop a novel flat-histogram Monte Carlo algorithm for simulating statistical ensembles of noninteracting fermions coupled to auxiliary classical fields.
• To enable direct computation of the partition function at all temperatures for these systems.

Main Methods:

• The algorithm utilizes the complete thermodynamic information from the full energy spectrum of noninteracting fermions during the sampling of the classical field configuration space.
• It employs a flat-histogram Monte Carlo approach to simulate the statistical ensemble.

Main Results:

• The developed algorithm successfully simulates the statistical ensemble, allowing direct acquisition of the partition function across the entire temperature range.
• The method was benchmarked against classical Ising and Potts models in 2D, and the Falicov-Kimball model, demonstrating its efficacy.

Conclusions:

• This flat-histogram Monte Carlo algorithm offers an efficient and direct method for obtaining the partition function and complete thermodynamic information for complex fermionic systems.
• The approach has broad applicability in many-body physics, including the study of materials and strongly correlated electrons.