Accuracy of the new pairing theory and its improvement

TL;DR

This paper introduces an improved pairing theory method based on Heisenberg equations, evaluates its accuracy against previous versions and variational methods, and compares computational efficiency using random interaction ensembles.

Contribution

An improved pairing theory method is developed with more careful derivation, enhancing accuracy and efficiency over previous versions and variational approaches.

Findings

The improved method shows higher accuracy than the original version.

The new approach is computationally more efficient.

Statistical evaluation demonstrates its robustness across random interactions.

Abstract

Recently I proposed a new method for solving the pairing Hamiltonian with the pair-condensate wavefunction ansatz based on the Heisenberg equations of motion for the density matrix operators. In this work an improved version is given by deriving the relevant equations more carefully. I evaluate both versions in a large ensemble with random interactions, and the accuracy of the methods is given statistically in terms of root-mean-square derivations from the exact results. The widely used variational calculation is also done and the results and computing-time costs are compared.