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 $2\le L\le N$. We confirm the structure of low- $L$ states proposed by Mottelson as mainly single-particle excitations with two or three units of angular momentum.