  By using a state of art tensor network state method, we study the
ground-state phase diagram of an extended Bose-Hubbard model on the square
lattice with frustrated next-nearest neighboring tunneling. In the hardcore
limit, tunneling frustration stabilizes a peculiar half supersolid (HSS) phase
with one sublattice being superfluid and the other sublattice being Mott
Insulator away from half filling. In the softcore case, the model shows very
rich phase diagrams above half filling, including three different types of
supersolid phases depending on the interaction parameters. The considered model
provides a promising route to experimentally search for novel stable supersolid
state induced by frustrated tunneling in below half filling region with dipolar
atoms or molecules.
