Novel Extrapolation Method in the Monte Carlo Shell Model

TL;DR

This paper introduces a new extrapolation technique based on energy variance in the Monte Carlo shell model, enabling more accurate estimation of energies and observables for complex nuclear systems.

Contribution

It develops a novel energy variance extrapolation method with an efficient formula for deformed Slater determinants, extending applicability beyond current exact diagonalization limits.

Findings

Successfully applied to $^{56}$Ni full $pf$-shell calculation.

Demonstrated feasibility for $^{64}$Ge beyond current exact diagonalization.

Provides a practical tool for large-scale nuclear structure calculations.

Abstract

We propose an extrapolation method utilizing energy variance in the Monte Carlo shell model in order to estimate the energy eigenvalue and observables accurately. We derive a formula for the energy variance with deformed Slater determinants, which enables us to calculate the energy variance efficiently. The feasibility of the method is demonstrated for the full $pf$-shell calculation of $^{56}$Ni, and the applicability of the method to a system beyond current limit of exact diagonalization is shown for the $pf$+$g_{9/2}$-shell calculation of $^{64}$Ge.