Density functional for pairing with particle number conservation

TL;DR

This paper introduces a new density functional for pairing in finite many-body systems, which generalizes BCS and matches exact solutions well across different particle numbers and couplings.

Contribution

A novel functional based on the projected BCS framework that offers an alternative to the Variation After Projection method for pairing correlations.

Findings

Excellent agreement with exact solutions across tested cases

Generalizes BCS approach for finite systems

Applicable to various particle numbers and coupling strengths

Abstract

In this work, a new functional is introduced to treat pairing correlations in finite many-body systems. Guided by the projected BCS framework, the energy is written as a functional of occupation numbers. It is shown to generalize the BCS approach and to provide an alternative to Variation After Projection framework. Illustrations of the new approach are given for the pairing Hamiltonian for various particle numbers and coupling strengths. In all case, a very good agreement with the exact solution is found.