Thermal properties of many-electron systems: An integral formulation of density-functional theory

A new approach for the calculation of thermal properties of many-electron systems is proposed via an integral formulation of the Mermin-Kohn-Sham finite-temperature density-functional theory. The electron density of a thermal-equilibrium state can be determined by solving self-consistently equations for the electron density without using orbitals. Exchange and correlation effects are incorporated. In place of the set of the single-electron equations, the total electron density is explicitly expressed in terms of the Kohn-Sham effective local potential through multidimensional integrations. The development is based on the first-order density matrix as obtained from the one-body Green’s function in polygonal and Fourier path-integral representations. The formulation can also be applied to general fermions.