Description of Pairing correlation in Many-Body finite systems with density functional theory

TL;DR

This paper analyzes the development of a new pairing functional in density functional theory for finite many-body systems, demonstrating its accuracy and applicability through detailed theoretical derivation and benchmarking against exact solutions.

Contribution

It introduces an explicit pairing functional based on natural orbitals and occupancies, derived via a 1/N expansion from the BCS approach, and validates it through extensive benchmarking.

Findings

Functional achieves less than 1% deviation from exact energies

Good agreement in various particle numbers and coupling strengths

Applicable to systems with uniform and random level spacings

Abstract

Different steps leading to the new functional for pairing based on natural orbitals and occupancies proposed in ref. [D. Lacroix and G. Hupin, arXiv:1003.2860] are carefully analyzed. Properties of quasi-particle states projected onto good particle number are first reviewed. These properties are used (i) to prove the existence of such a functional (ii) to provide an explicit functional through a 1/N expansion starting from the BCS approach (iii) to give a compact form of the functional summing up all orders in the expansion. The functional is benchmarked in the case of the picked fence pairing Hamiltonian where even and odd systems, using blocking technique are studied, at various particle number and coupling strength, with uniform and random single-particle level spacing. In all cases, a very good agreement is found with a deviation inferior to 1% compared to the exact energy.