  We investigate exotic supersolid phases in the extended Bose-Hubbard model
with infinite projected entangled-pair state, numerical exact diagonalization,
and mean-field theory. We demonstrate that many different supersolid phases can
be generated by changing signs of hopping terms, and the interactions along
with the frustration of hopping terms are important to stabilize those
supersolid states. We argue the effect of frustration introduced by the
competition of hopping terms in the supersolid phases from the mean-field point
of view. This helps to give a clearer picture of the background mechanism for
underlying superfluid/supersolid states to be formed. With this knowledge, we
predict and realize the $d$-wave superfluid, which shares the same pairing
symmetry with high-$T_c$ materials, and its extended phases. We believe that
our results contribute to preliminary understanding for desired target phases
in the real-world experimental systems.
