Pair-correlation ansatz for the ground state of interacting bosons in an arbitrary one-dimensional potential

We derive and describe a very accurate variational scheme for the ground state of the system of a few ultra-cold bosons confined in one-dimensional traps of arbitrary shapes. It is based on assumption that all inter-particle correlations have two-body nature. By construction, the proposed ansatz is exact in the noninteracting limit, exactly encodes boundary conditions forced by contact interactions, and gives full control on accuracy in the limit of infinite repulsions. We show its efficiency in a whole range of intermediate interactions for different external potentials. Our results manifest that for generic non-parabolic potentials mutual correlations forced by interactions cannot be captured by distance-dependent functions.

Automated summary

This study presents a highly accurate variational scheme for describing the ground state of a system of a few ultra-cold bosons confined in one-dimensional traps of arbitrary shapes. The proposed method shows efficiency across a range of intermediate interactions under different external potentials. The results highlight that mutual correlations forced by interactions in generic non-parabolic potentials cannot be captured by distance-dependent functions.