Evaluation of overlaps between arbitrary Fermionic quasiparticle vacua

TL;DR

This paper presents a new mathematical formula using Pfaffians to accurately evaluate overlaps between complex fermionic quasiparticle states, improving calculations in nuclear physics models.

Contribution

It extends previous overlap formulas to the most general case, including blocked states and odd systems, enabling more precise nuclear structure computations.

Findings

Derived a Pfaffian-based expression for quasiparticle vacuum overlaps

Validated the method with realistic angular-momentum-restored calculations

Enhanced the accuracy of overlaps in complex nuclear models

Abstract

We derive an expression that allows for the unambiguous evaluation of the overlap between two arbitrary quasiparticle vacua, including its sign. Our expression is based on the Pfaffian of a skew-symmetric matrix, extending the formula recently proposed by [L. M. Robledo, Phys. Rev. C 79, 021302(R) (2009)] to the most general case, including the one of the overlap between two different blocked n-quasiparticle states for either even or odd systems. The powerfulness of the method is illustrated for a few typical matrix elements that appear in realistic angular-momentum-restored Generator-Coordinate Method calculations when breaking time-reversal invariance and using the full model space of occupied single-particle states.