  We study a system of hardcore boson on a one-dimensional lattice with
frustrated next-nearest neighbor hopping and nearest neighbor interaction. At
half filling, for equal magnitude of nearest and next-nearest neighbor hopping,
the ground state of this system exhibits a first order phase transition from a
Bond-Ordered (BO) solid to a Charge-Density-Wave(CDW) solid as a function of
the nearest neighbor interaction. Moving away from half filling we investigate
the system at incommensurate densities, where we find a SuperSolid (SS) phase
which has concurrent off-diagonal long range order and density wave order which
is unusual in a system of hardcore bosons in one dimension. Using the
finite-size Density-Matrix Renormalization Group (DMRG) method, we obtain the
complete phase diagram for this model.
