Quantum spin models with long-range interactions and tunnelings: a quantum Monte Carlo study

Abstract

We use a quantum Monte Carlo method to investigate various classes of 2D spin\nmodels with long-range interactions at low temperatures. In particular, we\nstudy a dipolar XXZ model with U(1) symmetry that appears as a hard-core boson\nlimit of an extended Hubbard model describing polarized dipolar atoms or\nmolecules in an optical lattice. Tunneling, in such a model, is short-range,\nwhereas density-density couplings decay with distance following a cubic power\nlaw. We investigate also an XXZ model with long-range couplings of all three\nspin components - such a model describes a system of ultracold ions in a\nlattice of microtraps. We describe an approximate phase diagram for such\nsystems at zero and at finite temperature, and compare their properties. In\nparticular, we compare the extent of crystalline, super?uid, and supersolid\nphases. Our predictions apply directly to current experiments with mesoscopic\nnumbers of polar molecules and trapped ions.\n