Pairing in finite systems: beyond the HFB theory

TL;DR

This paper introduces a systematic approach to restore symmetries and extend configuration spaces in the HFB theory for finite quantum fermion systems, improving spectroscopic property descriptions.

Contribution

It develops a general method using pfaffian formulas for matrix elements and a gradient method for constrained solutions, enhancing the HFB approximation's accuracy.

Findings

Unambiguous sign determination of matrix elements using pfaffian formulas

Effective symmetry restoration and configuration space extension methods

Application to systems with odd particle numbers

Abstract

The Hartree-Fock-Bogoliubov approximation is very useful for treating both long- and short-range correlations in finite quantum fermion systems, but it must be extended in order to describe detailed spectroscopic properties. One problem is the symmetry-breaking character of the HFB approximation. We present a general and systematic way to restore symmetries and to extend the configuration space using pfaffian formulas for the many-body matrix elements. The advantage of those formulas is that the sign of the matrix elements is unambiguously determined. It is also helpful to extend the space of configurations by constraining the HFB solutions in some way. A powerful method for finding these constrained solutions is the gradient method, based on the generalized Thouless transformation. The gradient method also preserves the number parity of the Bogoliubov transformation, which facilitates the application of the theory to systems with odd particle number.