Fluctuating local field approach to free energy of one-dimensional molecules with strong collective electronic fluctuations

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 nonperturbative 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 one 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 Neél temperature. We further demonstrate that the mean-field result can be even more improved introducing a multimode FLF scheme that additionally takes into account subleading fluctuations. Possible applications for the thermodynamics of real molecules are also discussed.