Odd-particle systems in the shell model Monte Carlo: circumventing a sign problem

TL;DR

This paper presents a new shell model Monte Carlo method that overcomes the sign problem for odd-particle systems, enabling accurate calculation of ground-state energies and pairing gaps in nuclei.

Contribution

The authors introduce a novel approach using imaginary-time Green's functions to bypass the sign problem in odd-particle shell model Monte Carlo simulations.

Findings

Successfully calculated pairing gaps in iron nuclei

Results agree well with experimental data

Method extends Monte Carlo applicability to odd systems

Abstract

We introduce a novel method within the shell model Monte Carlo approach to calculate the ground-state energy of a finite-size system with an odd number of particles by using the asymptotic behavior of the imaginary-time single-particle Green's functions. The method circumvents the sign problem that originates from the projection on an odd number of particles and has hampered direct application of the shell model Monte Carlo method to odd-particle systems. We apply this method to calculate pairing gaps of nuclei in the iron region. Our results are in good agreement with experimental pairing gaps.