Field theoretical representation of the Hohenberg-Kohn free energy for fluids

TL;DR

This paper develops a field theoretical integral representation of the Hohenberg-Kohn free energy for fluids, enabling perturbative calculations beyond Gaussian approximation in density functional theory.

Contribution

It derives a Hamiltonian including entropy terms from the grand partition function, enhancing the analytical tools for DFT in fluid systems.

Findings

Provides a new Hamiltonian formulation for density functional free energy.

Demonstrates the utility of the representation for perturbative calculations.

Shows consistency with existing DFT formulations.

Abstract

To go beyond Gaussian approximation to the Hohenberg-Kohn free energy playing the key role in the density functional theory (DFT), the density functional \textit{integral} representation would be relevant, because field theoretical approach to perturbative calculations becomes available. Then the present letter first derives the associated Hamiltonian of density functional, explicitly including logarithmic entropy term, from the grand partition function expressed by configurational integrals. Moreover, two things are done so that the efficiency of the obtained form may be revealed: to demonstrate that this representation facilitates the field theoretical treatment of the perturbative calculation, and further to compare our perturbative formulation with that of the DFT.