Auxiliary Field Quantum Monte Carlo for Dilute Neutrons on the Lattice

TL;DR

This paper adapts constrained path Auxiliary Field Quantum Monte Carlo to study dilute neutron systems on a lattice, benchmarking against known models and extending to nuclear physics applications.

Contribution

It introduces a lattice AFQMC approach for nuclear systems, bridging condensed matter techniques with nuclear physics.

Findings

Benchmark results align with known Hubbard model calculations.

Successfully reproduces scattering length and effective range for nuclear interactions.

Initial neutron system calculations demonstrate method viability.

Abstract

We employ constrained path Auxiliary Field Quantum Monte Carlo (AFQMC) in the pursuit of studying physical nuclear systems using a lattice formalism. Since AFQMC has been widely used in the study of condensed-matter systems such as the Hubbard model, we benchmark our method against published results for both one- and two-dimensional Hubbard model calculations. We then turn our attention to cold-atomic and nuclear systems. We use an onsite contact interaction that can be tuned in order to reproduce the known scattering length and effective range of a given interaction. Developing this machinery allows us to extend our calculations to study nuclear systems within a lattice formalism. We perform initial calculations for a range of nuclear systems from two- to few-body neutron systems.