An efficient method to evaluate energy variances for extrapolation methods

TL;DR

This paper introduces a computationally efficient method for evaluating energy variances in many-body nuclear calculations, significantly reducing the scaling complexity and enabling more practical extrapolation to eigenvalues.

Contribution

A new method for energy variance evaluation that depends on the number of particles and single-particle orbits, improving computational efficiency over existing approaches.

Findings

The new method scales with the number of particles and orbits, not single-particle states.

Application to helium-4 demonstrates the method's effectiveness.

Reduces computational complexity in energy variance calculations.

Abstract

The energy variance extrapolation method consists in relating the approximate energies in many-body calculations to the corresponding energy variances and inferring eigenvalues by extrapolating to zero variance. The method needs a fast evaluation of the energy variances. For many-body methods that expand the nuclear wave functions in terms of deformed Slater determinants, the best available method for the evaluation of energy variances scales with the sixth power of the number of single-particle states. We propose a new method which depends on the number of single-particle orbits and the number of particles rather than the number of single-particle states. We discuss as an example the case of ${}^4He$ using the chiral N3LO interaction in a basis consisting up to 184 single-particle states.