Three and Four Harmonically Trapped Particles in an Effective Field Theory Framework

TL;DR

This paper investigates few-fermion systems in a harmonic trap using an effective field theory approach, demonstrating improved convergence with higher-order corrections and providing accurate results at unitarity and finite scattering lengths.

Contribution

It introduces a systematic EFT framework for few-fermion systems in a trap, including higher-order corrections, and compares results with exact and other numerical methods.

Findings

Excellent agreement with exact solutions for three-fermion systems.

Improved convergence with next-to-leading order corrections.

Observation of structural changes in the three-body ground state at positive scattering length.

Abstract

We study systems of few two-component fermions interacting via short-range interactions within a harmonic-oscillator trap. The dominant interactions, which are two-body, are organized according to the number of derivatives and defined in a two-body truncated model space made from a bound-state basis. Leading-order (LO) interactions are solved for exactly using the formalism of the No-Core Shell Model, whereas corrections are treated as many-body perturbations. We show explicitly that next-to-LO and next-to-next-to-LO interactions improve convergence as the model space increases. We present results at unitarity for three- and four-fermion systems, which show excellent agreement with the exact solution (for the three-body problem) and results obtained by others methods (in the four-body case). We also present results for finite scattering lengths and non-zero range of the interaction, including (at positive scattering length) observation of a change in the structure of the three-body ground state and extraction of the atom-dimer scattering length.