  We present a theory for the localization of three-dimensional vortex lines or
two-dimensional bosons with short-ranged repulsive interaction which are
competing for a single columnar defect or potential well. For two vortices we
use a necklace model approach to find a new kind of delocalization transition
between two different states with a single bound particle. This
exchange-delocalization transition is characterized by the onset of vortex
exchange on the defect for sufficiently weak vortex-vortex repulsion or
sufficiently weak binding energy corresponding to high temperature. We
calculate the transition point and order of the exchange-delocalization
transition. A generalization of this transition to arbitrary vortex number is
proposed.
