Nuclear Lattice Simulations using Symmetry-Sign Extrapolation

TL;DR

This paper introduces the symmetry-sign extrapolation method to extend lattice Monte Carlo simulations of nuclear systems, overcoming sign oscillation issues and enabling studies of more complex nuclei.

Contribution

The paper presents a novel symmetry-sign extrapolation technique leveraging SU(4) symmetry to mitigate sign problems in nuclear lattice simulations.

Findings

Successfully calculated ground-state energies of $^{12}$C, $^6$He, and $^6$Be.

Demonstrated potential for studying neutron-rich and asymmetric nuclear matter.

Extended the applicability of Monte Carlo methods to nuclei with severe sign oscillations.

Abstract

Projection Monte Carlo calculations of lattice Chiral Effective Field Theory suffer from sign oscillations to a varying degree dependent on the number of protons and neutrons. Hence, such studies have hitherto been concentrated on nuclei with equal numbers of protons and neutrons, and especially on the alpha nuclei where the sign oscillations are smallest. Here, we introduce the "symmetry-sign extrapolation" method, which allows us to use the approximate Wigner SU(4) symmetry of the nuclear interaction to systematically extend the Projection Monte Carlo calculations to nuclear systems where the sign problem is severe. We benchmark this method by calculating the ground-state energies of the $^{12}$C, $^6$He and $^6$Be nuclei, and discuss its potential for studies of neutron-rich halo nuclei and asymmetric nuclear matter.