SU(N) fermions in a one-dimensional harmonic trap

E. K. Laird, Z. Y. Shi, M. M. Parish, J. Levinsen

Research output: Contribution to journalArticleResearchpeer-review

Abstract

We conduct a theoretical study of SU(N) fermions confined by a one-dimensional harmonic potential. First, we introduce a 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.

Original languageEnglish
Article number032701
Number of pages13
JournalPhysical Review A
Volume96
Issue number3
DOIs
Publication statusPublished - 1 Sep 2017

Cite this

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title = "SU(N) fermions in a one-dimensional harmonic trap",
abstract = "We conduct a theoretical study of SU(N) fermions confined by a one-dimensional harmonic potential. First, we introduce a 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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SU(N) fermions in a one-dimensional harmonic trap. / Laird, E. K.; Shi, Z. Y.; Parish, M. M.; Levinsen, J.

In: Physical Review A, Vol. 96, No. 3, 032701, 01.09.2017.

Research output: Contribution to journalArticleResearchpeer-review

TY - JOUR

T1 - SU(N) fermions in a one-dimensional harmonic trap

AU - Laird, E. K.

AU - Shi, Z. Y.

AU - Parish, M. M.

AU - Levinsen, J.

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Y1 - 2017/9/1

N2 - We conduct a theoretical study of SU(N) fermions confined by a one-dimensional harmonic potential. First, we introduce a 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.

AB - We conduct a theoretical study of SU(N) fermions confined by a one-dimensional harmonic potential. First, we introduce a 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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