On the direct diagonalization method for a few particles trapped in harmonic potentials

TL;DR

This paper introduces a systematic method to enhance direct diagonalization calculations for few-particle systems in harmonic traps with contact interactions, using a renormalization approach benchmarked against existing numerical results.

Contribution

It presents a novel renormalization procedure based on the two-body problem to improve diagonalization results for few-particle systems in harmonic potentials.

Findings

The method effectively improves accuracy of diagonalization results.

Benchmarking shows good agreement with existing numerical data.

Applicable to systems with contact interactions in harmonic traps.

Abstract

We describe a procedure to systematically improve direct diagonalization results for few-particle systems trapped in one-dimensional harmonic potentials interacting by contact interactions. We start from the two-body problem to define a renormalization method for the interparticle interactions. The procedure is benchmarked with state-of-the-art numerical results for three and four symmetric fermions.