New and Practical Formulation for Overlaps of Bogoliubov Vacua.

B G Carlsson,J Rotureau

doi:10.1103/physrevlett.126.172501

Abstract

In this Letter, we present a new expression for the overlaps of wave functions in Hartree-Fock-Bogoliubov based theories. Starting from the Pfaffian formula by Bertsch etal. [1], 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 nonorthogonal many-body basis states.

Highlights

Introduction.—A very successful approach in the context of many-body theory is to incorporate correlation effects through symmetry breaking followed by restoration of symmetries [2]
The modulus of the overlap between two HFB vacua can be computed with the Onishi formula [12] leaving ambiguity on its sign
The matrix Vis written in terms of N=2 blocks of dimension 2 × 2 with elements (vi; −vi) where canonical basis v2i is the occupation probability state i

Summary

New and Practical Formulation for Overlaps of Bogoliubov Vacua

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, for methods dealing with superfluidity, symmetry restoration, and uses of nonorthogonal many-body basis states. Nuclear physics applications of HFB coupled with symmetry-restoration methods have allowed us to accurately describe a vast swath of nuclear properties such as binding energies, mean-square radii, deformation, and spectra. Under certain circumstances, such as for instance in the case of shape coexistence, it becomes necessary to include additional correlations between the quasiparticles. For vi 1⁄4 1, the level i is fully occupied whereas it is empty for vi 1⁄4 0. v0i and C0 in

Published by the American Physical Society

Introducing the diagonal matrix