SU(N) Fermions in a One-Dimensional Harmonic Trap

TL;DR

This paper introduces a new numerical method for analyzing SU(N) fermions in a one-dimensional harmonic trap, mapping the problem to a spin chain and exploring ground-state energies across interaction regimes.

Contribution

The study presents a novel numerical approach for solving the few-body problem, extends an existing ansatz to N-component systems, and analyzes ground-state energies for balanced SU(N) Fermi gases.

Findings

Accurate energy spectra obtained across all interaction strengths.

The spin-chain mapping is effective in the strong-coupling limit.

Ground-state energies converge rapidly with increasing atom number.

Abstract

We conduct a theoretical study of SU(N) fermions confined by a one-dimensional harmonic potential. Firstly, we introduce a new numerical approach for solving the trapped interacting few-body problem, by which one may obtain accurate energy spectra across the full range of interaction strengths. In the strong-coupling limit, we map the SU(N) Hamiltonian to a spin-chain model. We then show that an existing, extremely accurate ansatz - derived for a Heisenberg SU(2) spin chain - is extendable to these N-component systems. Lastly, we consider balanced SU(N) Fermi gases that have an equal number of particles in each spin state for N=2, 3, 4. In the weak- and strong-coupling regimes, we find that the ground-state energies rapidly converge to their expected values in the thermodynamic limit with increasing atom number. This suggests that the many-body energetics of N-component fermions may be accurately inferred from the corresponding few-body systems of N distinguishable particles.