Technical aspects of the evaluation of the overlap of Hartree- Fock- Bogoliubov wave functions

TL;DR

This paper discusses advanced computational techniques for evaluating overlaps between Hartree-Fock-Bogoliubov wave functions, including handling fully occupied orbitals, different bases, and practical pfaffian calculations.

Contribution

It introduces new formulas and methods for overlap evaluation, extending existing formalism to more complex cases with different bases and fully occupied orbitals.

Findings

Derived limits for fully occupied orbitals

Formulas for reducing problem dimensionality with empty orbitals

Practical methods for pfaffian evaluation and norm overlaps

Abstract

Several technical aspects concerning the evaluation of the overlap between two mean field wave functions of the Hartree Fock Bogoliubov type, are discussed. The limit when several orbitals become fully occupied is derived as well as the formula to reduce the dimensionality of the problem when exactly empty orbitals are present. The formalism is also extended to deal with the case where the bases of each of the wave functions are different. Several practical results concerning the evaluation of pfaffians as well as the canonical decomposition of norm overlaps are also discussed in the appendices.