Fluctuating local field approach to free energy of 1D molecules with strong collective electronic correlations

TL;DR

The paper introduces a Fluctuating Local Field (FLF) approach to accurately compute the free energy of 1D molecular systems with strong electronic correlations, improving upon mean-field methods by accounting for collective fluctuations.

Contribution

The paper develops a non-perturbative FLF method that enhances mean-field theory for 1D molecules, incorporating collective electronic fluctuations without assumptions on their magnitude.

Findings

FLF improves free energy estimates over mean-field below Neel temperature

Multi-mode FLF further refines results by including sub-leading fluctuations

Potential applications to thermodynamics of real molecular systems

Abstract

The impact of leading collective electronic fluctuations on a free energy of a prototype 1D model for molecular systems is considered within the recently developed Fluctuating Local Field (FLF) approach. The FLF method is a non-perturbative extension of a mean-field theory, where a self-consistent effective constant field is replaced by a fluctuating one. Integrating the fluctuating field out numerically exactly allows to account for collective electronic fluctuations mediated by this field without any assumptions on their magnitude, degree of nonlinearity, etc. Using a half-filled Hubbard ring as a benchmark system, we find that the FLF method noticeably improves a mean-field estimation for the free energy, in particular below the mean-field Ne\'el temperature. We further demonstrate that the mean-field result can be even more improved introducing a multi-mode FLF scheme that additionally takes into account sub-leading fluctuations. Possible applications for the thermodynamics of real molecules are also discussed.