A new effective interaction for the trapped Fermi gas

TL;DR

This paper introduces a new regularization method for the two-body interaction in trapped Fermi gases, significantly improving convergence in configuration-interaction calculations for small systems at the unitary limit.

Contribution

A novel regularization approach that achieves exponential convergence in the CI method for small Fermi systems at unitarity, enhancing computational efficiency and accuracy.

Findings

Exponential convergence with the new regularization for three and four particles.

Estimated ground-state energy of four-particle system as (5.05 +- 0.024)hbar omega.

Poor convergence observed with conventional regularization.

Abstract

We apply the configuration-interaction method to calculate the spectra of two-component Fermi systems in a harmonic trap, studying the convergence of the method at the unitary interaction limit. We find that for a fixed regularization of the two-body interaction the convergence is exponential or better in the truncation parameter of the many-body space. However, the conventional regularization is found to have poor convergence in the regularization parameter, with an error that scales as a low negative power of this parameter. We propose a new regularization of the two-body interaction that produces exponential convergence for systems of three and four particles. From the systematics, we estimate the ground-state energy of the four-particle system to be (5.05 +- 0.024)hbar omega.