Exotic phases of bosons in one dimensional optical lattices

Experimental advances over the last decade or so have made it possible
to create optical lattices of cold atoms. The study of interacting
bosonic and fermionic atoms in such lattices is currently a very
active area of research. In this talk, I will describe various
interesting phases that can be obtained in systems of interacting
bosons in one dimensional lattices. I will show that in the presence
of frustration and further neighbour hopping or interactions, it is
possible to obtain phases other than the usual superfluid and
featureless Mott phases. In particular, I will show that it is
possible for Mott phases with broken symmetry, Haldane-type phases and
"chiral" superfluid phases to exist in these systems. Time permitting,
I will also describe phases and phase transitions of bosons with spin
on optical lattices.