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Effect of Vortex Screening on the Bose Glass to Entangled Liquid Transition of Flux Lines in Superconductors

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 ($B = B_ϕ$). We also find a transition from a strongly pinned Bose glass for $B < B_ϕ$ to a weakly pinned Bose glass for $B > B_ϕ$ as the vortex density is varied.