Yrast line for weakly interacting trapped bosons

TL;DR

This paper numerically analyzes the yrast line of weakly interacting trapped bosons, revealing a smooth crossover to vortex states with no quantum phase transition and confirming theoretical models of low-L states.

Contribution

It provides a detailed numerical study of the yrast line for weakly interacting bosons, showing the smooth transition to vortex states and confirming theoretical predictions.

Findings

Smooth crossover between low and high angular momentum states.

Energy and wave functions are analytical functions of L.

Low-L states are mainly single-particle excitations.

Abstract

We compute numerically the yrast line for harmonically trapped boson systems with a weak repulsive contact interaction, studying the transition to a vortex state as the angular momentum L increases and approaches N, the number of bosons. The L=N eigenstate is indeed dominated by particles with unit angular momentum, but the state has other significant components beyond the pure vortex configuration. There is a smooth crossover between low and high L with no indication of a quantum phase transition. 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.