Convergence Properties of the Effective Theory for Trapped Bosons

TL;DR

This paper analyzes the convergence of an effective theory for trapped bosons with resonant interactions, focusing on contact interactions and error analysis for systems with up to six particles.

Contribution

It provides a detailed study of convergence properties and error analysis for effective theories of trapped bosons, including genuine and smeared contact interactions.

Findings

Convergence improves with increasing model space size.

Error analysis guides the extrapolation process.

Spectra for up to 6 bosons are accurately computed.

Abstract

We investigate few-boson systems with resonant interactions in a narrow harmonic trap within an effective theory framework. The size of the model space is identified with the effective theory cutoff. In the universal regime, the interactions of the bosons can be approximated by contact interactions. We investigate the convergence properties of genuine and smeared contact interactions as the size of the model space is increased and present a detailed error analysis. The spectra for few-boson systems with up to 6 identical particles are calculated by combining extrapolations in the cutoff and in the smearing parameter.