  We study the Wigner crystal melting in a two dimensional quantum system of
particles interacting via the 1/r Coulomb potential. We use quantum Monte Carlo
methods to calculate its phase diagram, locate the Wigner crystal region, and
analyze its instabilities towards the liquid phase. We discuss the role of
quantum effects in the critical behavior of the system, and compare our
numerical results with the classical theory of melting, and the microemulsion
theory of frustrated Coulomb systems. We find a Pomeranchuk effect much larger
then in solid helium. In addition, we find that the exponent for the algebraic
decay of the hexatic phase differs significantly from the Kosterilitz-Thouless
theory of melting. We search for the existence of mesoscopic phases and find
evidence of metastable bubbles but no mesoscopic phase that is stable in
equilibrium.
