High-fidelity pseudopotentials for the contact interaction

TL;DR

This paper introduces a new family of smooth pseudopotentials that accurately replicate the scattering properties of the contact interaction, improving numerical efficiency in modeling ultracold atomic gases.

Contribution

A novel family of pseudopotentials is proposed that closely match the contact interaction's scattering phase shifts and are smoother for enhanced computational performance.

Findings

Pseudopotentials reproduce contact interaction phase shifts with high accuracy.

Smooth pseudopotentials significantly improve numerical calculation efficiency.

Outperform traditional models like the square well potential.

Abstract

The contact interaction is often used in modeling ultracold atomic gases, although it leads to pathological behavior arising from the divergence of the many-body wavefunction when two particles coalesce. This makes it difficult to use this model interaction in quantum Monte Carlo and other popular numerical methods. Researchers therefore model the contact interaction with pseudopotentials, such as the square well potential, whose scattering properties deviate markedly from those of the contact potential. In this article, we propose a family of pseudopotentials that reproduce the scattering phase shifts of the contact interaction up to a hundred times more accurately than the square well potential. Moreover, the pseudopotentials are smooth, resulting in significant improvements in efficiency when used in numerical calculations.