The two-dimensional Wigner crystal (WC) occurs in the strongly interacting regime of a two-dimensional electron gas (2DEG). The nature of the quantum melting of the WC has long been studied but is still poorly understood. We study the quantum dynamics of point defects (interstitials and vacancies) in a WC using the semi-classical instanton method that is asymptotically exact at low density, i.e., in the r_s -> \infty limit. The resulting semi-classical expression for the interstitial energy vanishes at r_s = r_mit signaling a possible self-doping instability of a WC to a partially melted WC for some range of r_s below r_mit. We thus propose that there exists a “metallic electron crystal” phase of the two-dimensional electron gas at intermediate densities between a low-density insulating WC and a high-density Fermi fluid. I will also discuss magnetic correlations induced by kinetic processes of interstitials and vacancies. Finally, if time permits, I will also talk about a more exotic resonating-valence-bond polaron induced by a hole-motion in an infinite U Hubbard model on a non-bipartite lattice.
