Superfluids, supersolids and Mott insulators on the triangular lattice

  Anton Burkov Harvard

  Interest in the behavior of interacting bosons on two-dimensional lattices has recently been revived by the experimental realization of superfluid-insulator transition of cold atoms in an optical lattice. Such models are also interesting from a broader prospective since they provide a simpler context to explore general aspects of conducting-insulating transitions of electrons. I will talk about our recent study of the interplay between Mott localization and geometrical frustration in a system of interacting bosons on the triangular lattice. Frustration prevents localization into simple ordered states, that can be determined by minimizing only the interaction energy. A variety of unconventional states thus become possible, notably supersolids and valence bond ordered insulators. I will describe a general phenomenological theory of these states, based on a duality transformation from bosons to vortices and compare this theory with numerical simulations.