Effective Theory for Trapped Few-Fermion Systems

TL;DR

This paper develops an effective field theory approach for few-fermion systems in traps, accurately calculating energy spectra and demonstrating the method's broad applicability to various regimes and particle types.

Contribution

It introduces a general effective interaction framework for few- and many-body calculations in a no-core shell model, with successful results for three- and four-fermion systems.

Findings

Three-fermion results within 10% of semi-analytical values in the unitary limit.

Method can be extended to other regimes, particles, and species.

Observed possible parity inversion in three-fermion ground state at large trap sizes.

Abstract

We apply the general principles of effective field theories to the construction of effective interactions suitable for few- and many-body calculations in a no-core shell model framework. We calculate the spectrum of systems with three and four two-component fermions in a harmonic trap. In the unitary limit, we find that three-particle results are within 10% of known semi-analytical values even in small model spaces. The method is very general, and can be readily extended to other regimes, more particles, different species (e.g., protons and neutrons in nuclear physics), or more-component fermions (as well as bosons). As an illustration, we present calculations of the lowest-energy three-fermion states away from the unitary limit and find a possible inversion of parity in the ground state in the limit of trap size large compared to the scattering length. Furthermore, we investigate the lowest positive-parity states for four fermions, although we are limited by the dimensions we can currently handle in this case.