Numerical study of vortex matter using the Bose model: First-order   melting and entanglement
  We present an extensive numerical study of vortex matter using the mapping to 2D bosons and Path-Integral Monte Carlo simulations. We find a first-order vortex lattice melting transition into an entangled vortex liquid. The jumps in entropy and density are consistent with experimental results on YBCO. The liquid is denser than the lattice and has a correlation length l_z approx 1.7 epsilon a_0 in the direction parallel to the field. In the language of bosons we find a sharp quantum phase transition from a Wigner crystal to a superfluid, even in the case of logarithmic interaction. We also measure the excitation spectrum of the Bose system and find the roton minimum to be insensitive to the range of the interaction. 
H. Nordborg, G. Blatter