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 two-dimensional 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 YBa₂Cu₃O_7-δ. The liquid is denser than the lattice and has a correlation length lz≈1.7εa₀ 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.