  Polar molecules in geometrically frustrated lattices may result in a very
rich landscape of quantum phases, due to the non-trivial interplay between
frustration, and two- and possibly three-body inter-site interactions. In this
paper, we illustrate this intriguing physics for the case of hard-core polar
molecules in frustrated triangular ladders. Whereas commensurate lattice
fillings result in gapped phases with bond-order and/or density-wave order, at
incommensurate fillings we find chiral-, two-component-, and pair-superfluids.
We show as well that, remarkably, polar molecules in frustrated lattices allow,
for the first time to our knowledge, for the observation of bond-ordered
supersolids.
