Pair Densities, Particle Number Fluctuations, and a Generalized Density Functional Theory

P. Ziesche

Katsuhiko Higuchi, Masahiko Higuchi

The pair-density functional theory for the superconductor (SC-PDFT) is one of first-principles theories for the superconductor.The feature of the SC-PDFT is that the fluctuation of the particle number of the superconducting state can be reproduced via the pair-density (PD) and electron density (ED).In this paper, we present a calculation scheme for the SC-PDFT.Specifically, in order to construct a calculation scheme, the searching region for PDs and EDs is devised with a reference to results of the uniform system, and the entropy functional is developed in a functional form in terms of the PD and ED.

Katsuhiko Higuchi, Masahiko Higuchi

Berthold‐Georg Englert, Heinz K. H. Siedentop, Martin-Isbjörn Trappe

Katsuhiko Higuchi, Eina Miki, Masahiko Higuchi

We show that the diagonal elements of the second-order reduced density matrix (RDM2) can be chosen as basic variables for describing the superconducting state, instead of the off-diagonal elements of the RDM2 that are usually adopted as basic variables in the density functional scheme. The diagonal elements of the RDM2 are called pair-density (PD), which is explicitly related to the fluctuation of the particle number of the system. In this paper, we argue that the fluctuation of the particle number can become an indication of the superconducting state, and that the density functional scheme in which the PD is chosen as a basic variable would be a promising first-principles theory for superconductors.

Denis Lacroix A, Guillaume Hupin

A functional theory based on single-particle occupation numbers is developed for pairing. This functional, that generalizes the Bardeen-Cooper-Schrieffer approach, directly incorporates corrections due to particle number conservation. The functional is benchmarked with the pairing Hamiltonian and reproduces perfectly the energy for any particle number and coupling.