A new and practical formulation for overlaps of Bogoliubov vacua

TL;DR

This paper introduces a new, exact, and stable formula for calculating overlaps of wavefunctions in Hartree-Fock-Bogoliubov theories, enhancing precision and versatility in superfluid and symmetry restoration methods.

Contribution

A novel formulation for overlaps of Bogoliubov vacua derived from the Pfaffian approach, improving computational stability and accuracy.

Findings

Enhanced numerical stability in overlap calculations

Increased precision in superfluidity and symmetry restoration methods

Applicable to chemical, atomic, and nuclear physics applications

Abstract

In this letter we present a new expression for the overlaps of wavefunctions in Hartree-Fock-Bogoliubov based theories. Starting from the Pfaffian formula by Bertsch et al (Phys. Rev. Lett. 108,042505 (2012)), an exact and computationally stable formula for overlaps is derived. We illustrate the convenience of this new formulation with a numerical application in the context of the particle-number projection method. This new formula allows for substantially increased precision and versatility in chemical, atomic, and nuclear physics applications, particularly for methods dealing with superfluidity, symmetry restoration and uses of non-orthogonal many-body basis states.