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.
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