The vortex system in a high- $T_c$ superconductor has been studied numerically using the mapping to 2D bosons and the path-integral Monte Carlo method. We find a single first-order transition from an Abrikosov lattice to an entangled vortex liquid. The transition is characterized by an entropy jump $\Delta S\approx {0.4k}_B$ per vortex and layer (parameters for ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_7$) and a Lindemann number $c_L\approx 0.25$. The increase in density at melting is given by $\Delta \rho \approx 6.0\times {10}^{-4\mathrm{}}/\lambda (T{)}^2$. The vortex liquid corresponds to a bosonic superfluid, with ${\rho }_s=\rho$ even in the limit $\lambda \to \infty$.

• Received 2 December 1996

DOI:https://doi.org/10.1103/PhysRevLett.79.1925