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arXiv · 1707.07781

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

E. K. Laird·Z. -Y. Shi·M. M. Parish·J. Levinsen
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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.

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E. K. Laird, Z. -Y. Shi, M. M. Parish, J. Levinsen. 2018-05-01. SU(N) Fermions in a One-Dimensional Harmonic Trap. https://doi.org/10.1103/physreva.96.032701

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