Pairing Correlations in Finite Systems: From the weak to the strong fluctuations regime

TL;DR

This paper develops a method to accurately describe pairing correlations in finite systems across different regimes, providing a versatile tool for complex quantum systems.

Contribution

It formulates the Particle Number Projected Generator Coordinate Method for the pairing Hamiltonian, enabling precise solutions in various pairing regimes.

Findings

Reproduces exact solutions in all pairing regimes

Analyzes wave function dependence on collective coordinates

Offers a simple yet effective approach for complex Hamiltonians

Abstract

The Particle Number Projected Generator Coordinate Method is formulated for the pairing Hamiltonian in a detailed way in the projection after variation and the variation after projection methods. The dependence of the wave functions on the generator coordinate is analyzed performing numerical applications for the most relevant collective coordinates. The calculations reproduce the exact solution in the weak, crossover and strong pairing regimes. The physical insight of the Ansatz and its numerical simplicity make this theory an excellent tool to study pairing correlations in complex situations and/or involved Hamiltonians.