Lattice methods for strongly interacting many-body systems

TL;DR

This paper reviews recent advances in applying lattice field theory methods, traditionally used in quantum chromodynamics, to study strongly interacting non-relativistic many-body systems at zero temperature, highlighting new techniques and results.

Contribution

It provides an overview of recent developments in lattice methods for non-relativistic many-body physics, including algorithms, observables, and systematic effects, with specific results on fermions at unitarity.

Findings

Selected results on ground- and excited-state properties of fermions at unitarity

Discussion of sampling algorithms and systematic effects

Overview of lattice group theory methods

Abstract

Lattice field theory methods, usually associated with non-perturbative studies of quantum chromodynamics, are becoming increasingly common in the calculation of ground-state and thermal properties of strongly interacting non-relativistic few- and many-body systems, blurring the interfaces between condensed matter, atomic and low-energy nuclear physics. While some of these techniques have been in use in the area of condensed matter physics for a long time, others, such as hybrid Monte Carlo and improved effective actions, have only recently found their way across areas. With this topical review, we aim to provide a modest overview and a status update on a few notable recent developments. For the sake of brevity we focus on zero-temperature, non-relativistic problems. After a short introduction, we lay out some general considerations and proceed to discuss sampling algorithms, observables, and systematic effects. We show selected results on ground- and excited-state properties of fermions in the limit of unitarity. The appendix contains details on group theory on the lattice.