In a seminal paper, Tanatar and Ceperley (1989) found the critical value of the electronic density at which a two dimensional electron gas cristallizes (into a hexagonal Wigner crystal). Their study of the quantum melting of the Wigner crystal used a fixed node quantum Monte-Carlo approach which I will revisit in this seminar. In addition to the two already known phases (Fermi liquid at large density and Wigner crystal at low density), we find a third stable phase at intermediate values of the density. The third phase has hybrid behaviors in between a liquid and a solid. This hybrid phase has the nodal structure of a Slater determinant constructed out of the bands of a triangular lattice. (Ref: cond-mat/0406600).

SPEC, CEA/Saclay