  We study the phase diagram of flux lines in superconductors with columnar
pins. Based on numerical exact diagonalisation simulations on small clusters,
we get two phases of vortices: A low temperature pinned glass with diverging
tilt modulus and a high temperature delocalised entangled vortex liquid. For
random potential disorder we find a new phase transition temperature $T_{\rm
BG}$ from a pinned Bose glass to an entangled liquid that reduces with
increasing vortex density. This occurs primarily because vortices screen the
disorder potential and generate an effective weaker random potential with
increasing vortex density. For a fixed fraction of randomly placed attractive
columnar pins of strength $V_{\rm pin}$, we find a Mott insulating phase when
the vortex density exactly matches the number of pins ($B = B_{\phi}$). We also
find a transition from a strongly pinned Bose glass for $B < B_{\phi}$ to a
weakly pinned Bose glass for $B > B_{\phi}$ as the vortex density is varied.
