Abstract:
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.