  We study a system of interacting electrons on a one-dimensional quantum ring
using exact diagonalization and the variational quantum Monte Carlo method. We
examine the accuracy of the Slater-Jastrow -type many-body wave function and
compare energies and pair distribution functions obtained from the two
approaches. Our results show that this wave function captures most correlation
effects. We then study the smooth transition to a regime where the electrons
localize in the rotating frame, which for the ultrathin quantum ring system
happens at quite high electron density.
