Pfaffian formulation for matrix elements of three-body operators in multiple quasiparticle configurations

We present a Pfaffian formula to calculate matrix elements of three-body operators in symmetry-restoration beyond-mean-field methods, including the case of multiple quasiparticle (qp) configurations. Detailed derivation is provided and the validity of the new formula is checked numerically. The corresponding efficiency is discussed, which turns out to be about five times (one order of magnitude) higher than the conventional method when four (less than four) qp operators are considered.

Automated summary

A Pfaffian formula is proposed to calculate matrix elements of three-body operators in symmetry-restoration beyond-mean-field methods, including multiple qp configurations. Numerical checks show that the efficiency of the new formula is about five times higher than the conventional method when considering four or fewer qp operators.