  We investigate the interplay between commensurate lock-in and incommensurate
supersolid phases of the hardcore bosons at half-filling with anisotropic
nearest-neighbor hopping and repulsive interactions on triangular lattice. We
use numerical quantum and variational Monte Carlo as well as analytical
Schwinger boson mean-field analysis to establish the ground states and phase
diagram. It is shown that, for finite size systems, there exist a series of
jumps between different supersolid phases as the anisotropy parameter is
changed. The density ordering wavevectors are locked to commensurate values and
jump between adjacent supersolids. In the thermodynamic limit, however, the
magnitude of these jumps vanishes leading to a continuous set of novel
incommensurate supersoild phases.
