Two interacting fermions in a 1D harmonic trap: matching the Bethe ansatz and variational approaches

Abstract

In this work, combining the Bethe ansatz approach with the variational principle, we calculate the ground state energy of the relative motion of a system of two fermions with spin up and down interacting via a delta-function potential in a 1D harmonic trap. Our results show good agreement with the analytical solution of the problem, and provide a starting point for the investigation of more complex few-body systems where no exact theoretical solution is available.

arXiv comment8 pages, 2 figures

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• A variational approach to repulsively interacting three-fermion systems in a one-dimensional harmonic trap
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• Variational Bethe Ansatz approach for dipolar one-dimensional bosons
• Reduced density matrix approach to ultracold few-fermion systems in one dimension
• Comparing models for the ground state energy of a trapped one-dimensional Fermi gas with a single impurity
• Inhomogeneous state of few-fermion superfluids
• Exploring exchange mechanisms with a cold atom gas
• Dynamical realization of magnetic states in a strongly interacting Bose mixture
• Computation of local exchange coefficients in strongly interacting one-dimensional few-body systems: local density approximation and exact results
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• Pair-correlation ansatz for the ground state of interacting bosons in an arbitrary one-dimensional potential
• One-particle spectral function singularities in a one-dimensional gas of spin-1/2 fermions with repulsive delta-function interaction
• Systematic interpolatory ansatz for one-dimensional polaron systems
• Composite Bosons Superposition Ansatz Approach to One-Dimensional Trapped Few-Fermion Systems