Anatomy of the quantum melting of the two dimensional Wigner crystal

The Fermi liquid-Wigner crystal transition in a two dimensional electronic system is revisited with a focus on the nature of the fixed node approximation done in quantum Monte Carlo calculations. Recently, we proposed (Phys. Rev. Lett. 94, 046801 (2005)) that for intermediate densities, a hybrid phase (with the symmetry of the crystal but otherwise liquid like properties) is more stable than both the liquid and the crystal phase. Here we confirm this result both in the thermodynamic and continuum limit. The liquid-hybrid transition takes place at rs=31.5 +/- 0.5. We find that the stability of the hybrid phase with respect to the crystal one is tightly linked to its delocalized nature. We discuss the implications of our results for various transition scenarii (quantum hexatic phase, supersolid, multiple exchange, microemulsions) proposed in the literature.