Lattice methods and the nuclear few- and many-body problem

TL;DR

This paper reviews lattice methods in nuclear physics, focusing on algorithms and formalisms for simulating few- and many-body nuclear systems using chiral effective field theory, including practical coding examples.

Contribution

It demonstrates the equivalence of four lattice formalisms and provides detailed algorithms and exercises for nuclear lattice simulations at leading order.

Findings

Four lattice formalisms are proven equivalent.

Provides algorithms for nuclear lattice simulations.

Includes coding examples and exercises.

Abstract

We begin with a brief overview of lattice calculations using chiral effective field theory and some recent applications. We then describe several methods for computing scattering on the lattice. After that we focus on the main goal, explaining the theory and algorithms relevant to lattice simulations of nuclear few- and many-body systems. We discuss the exact equivalence of four different lattice formalisms, the Grassmann path integral, transfer matrix operator, Grassmann path integral with auxiliary fields, and transfer matrix operator with auxiliary fields. Along with our analysis we include several coding examples and a number of exercises for the calculations of few- and many-body systems at leading order in chiral effective field theory.