Bose-Fermi solid and its quantum melting in an one-dimensional optical lattice

We investigate the quantum phase diagram of Bose-Fermi mixtures of ultracold dipolar particles trapped in one-dimensional optical lattices in the thermodynamic limit. With the presence of nearest-neighbor (N.N.) interactions, a long-ranged ordered crystalline phase (Bose-Fermi solid) is found stabilized between a Mott insulator of bosons and a band-insulator of fermions in the limit of weak inter-site tunneling ($J$). When $J$ is increased, such a Bose-Fermi solid can be quantum melted into a Bose-Fermi liquid through either a two-stage or a three-stage transition, depending on whether the crystalline order is dominated by the N.N. interaction between fermions or bosons. These properties can be understood as quantum competition between a pseudo-spin frustration and a pseudo-spin-charge separation, qualitatively different from the classical picture of solid-liquid phase transition.