Yrast Line for Weakly Interacting Trapped Bosons

We compute numerically the yrast line for harmonically trapped N-boson systems with a weak repulsive contact interaction, studying the transition to a vortex state as the angular momentum L increases and approaches N. There is a smooth crossover between low and high L with no indication of a quantum phase transition; at L = N there is a kink in the slope of the spectrum. Most strikingly, the energy and wave function appear to be analytical functions of L over the entire range 2≤L≤N. We confirm the structure of low- L states proposed by Mottelson as mainly single-particle excitations with two or three units of angular momentum.