Mathematical relations of the Onishi formula, Neergaard-Wust formula and the Pfaffian formula of Robledo’s

The Onishi formula was proposed about a half century ago for the evaluation of the Hartree-Fock-Bogoliubov norm overlap functions. However, the formula suffers from the so-called sign problem. Neergaard and Wust proposed an alternative formula in 1980s’ for the remedy of the problem, but their paper has been long ignored for unclear reasons. The new formula was proposed by Robledo in 2009, which is expressed in terms of the Pfaffian. Robledo’s formula was widely accepted and is applied to many computational studies.

We recently wrote a computer code to apply the Neergaard-Wust formula for practical cases, and confirmed that the method is as valid as Robledo’s. There are even cases in which Neergaard-Wust method surpasses the Pfaffian formula.

We extended our study to the mathematical investigation about these formulae.
Although many have believed that there are no connections among these formulae, we found a mathematical relations to connect them, which is the primary topic in our talk.