Construction of analytical many body wave functions for correlated bosons in a harmonic trap

TL;DR

This paper presents an analytical wave function for one-dimensional bosons in a harmonic trap, accurately capturing the transition from weak to strong interactions and matching numerical results.

Contribution

It introduces an explicit analytical wave function based on two-body states that works across interaction regimes for many bosons in a trap.

Findings

Accurately describes the interaction crossover in 1D bosonic systems

Wave function matches numerical calculations for energies and densities

Respects known limits at zero and infinite repulsion

Abstract

We develop an analytical many-body wave function to accurately describe the crossover of a one-dimensional bosonic system from weak to strong interactions in a harmonic trap. The explicit wave function, which is based on the exact two-body states, consists of symmetric multiple products of the corresponding parabolic cylinder functions, and respects the analytically known limits of zero and infinite repulsion for arbitrary number of particles. For intermediate interaction strengths we demonstrate, that the energies, as well as the reduced densities of first and second order, are in excellent agreement with large scale numerical calculations.