Structure of the number projected BCS wave function

TL;DR

This paper analyzes the structure of the number projected BCS wave function, comparing it with coupled clusters theory, and explores its limitations and potential improvements within an exactly solvable pairing model.

Contribution

It provides a detailed comparison of PBCS with CCT and suggests modifications to improve its description of non-superconducting regimes.

Findings

PBCS shares similarities with coupled clusters theory.

PBCS has limitations in non-superconducting regimes.

Proposed modifications could enhance PBCS accuracy.

Abstract

We study the structure of the number projected BCS (PBCS) wave function in the particle-hole basis, displaying its similarities with coupled clusters theory (CCT). The analysis of PBCS together with several modifications suggested by the CCT wave function is carried out for the exactly solvable Richardson model involving a pure pairing hamiltonian acting in a space of equally-spaced doubly-degenerate levels. We point out the limitations of PBCS to describe the non-superconducting regime and suggest possible avenues for improvement.