Circumventing the odd particle-number sign problem in the shell model Monte Carlo

TL;DR

This paper introduces the partition function extrapolation method (PFEM) to overcome the sign problem in shell model Monte Carlo calculations of odd-mass nuclei, enabling accurate ground-state energy determination.

Contribution

The paper develops and validates PFEM, a novel technique to extract ground-state energies of odd-mass nuclei from SMMC calculations despite the sign problem.

Findings

PFEM successfully estimates ground-state energies in heavy odd-mass nuclei.

The method is validated on heavy even-mass nuclei.

PFEM can be extended to other quantum many-body systems.

Abstract

The shell model Monte Carlo (SMMC) method is a powerful method for calculating exactly (up to statistical errors) thermal observables and statistical properties of atomic nuclei. However, its application has been limited by a sign problem at low temperatures that arises from the projection onto odd particle number even for good-sign interactions. Here, we develop a technique - the partition function extrapolation method (PFEM) - to extract the ground-state energy of an odd-mass nucleus from the excitation partition function calculated at temperatures at which this sign problem is moderate. We validate the PFEM in heavy even-mass nuclei and systematically calculate ground-state energies for isotopic chains of heavy odd-mass nuclei. The PFEM can be extended to other finite-size quantum many-body systems.