Simulation of Flux Lines with Columnar Pins: Bose Glass and Entangled Liquids

Using path integral Monte Carlo we simulate a 3D system of up to 1000 magnetic flux lines by mapping it onto interacting bosons in $(2+1)\mathrm{D}$. With increasing temperatures we find first order melting from an ordered solid to an entangled liquid signaled by a finite entropy jump and sharp discontinuities of the defect density and the structure factor $S\left(\mathbf{G}\right)$. For a particular density of strong columnar pins the crystal is transformed into a Bose glass phase with patches of crystalline order disrupted by the trapped vortices at the pinning sites but with no overall positional or orientational order. This glassy phase melts into a defected entangled liquid through a continuous transition.