Flux lattice melting, flux pinning, and superfluid density tensor of ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$

We calculate the flux lattice melting curve ${\mathit{T}}_{\mathit{M}}$(H) of ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ for a magnetic field H∥c, in good agreement with experiment without any free parameters. We expand the Ginzburg-Landau order parameter in products of lowest Landau levels in the a-b plane and Bloch states in the c direction, evaluating the relevant statistical averages by Monte Carlo simulation. With no pinning, the c component of the superfluid density tensor jumps to a finite value at the transition, but the transverse components remain zero, corresponding to the sliding freedom of the flux lattice. With pinning present, the in-plane components become finite also. Relevant experiments are discussed.