  We investigate the ground state phase diagram of hard-core boson system with
repulsive two-body and attractive three-body interactions in one-dimensional
optic lattice. When these two interactions are comparable and increasing the
hopping rate, physically intuitive analysis indicates that there exists an
exotic phase separation regime between the solid phase with charge density wave
order and superfluid phase. We identify these phases and phase transitions by
numerically analyzing the density distribution, structure factor of
density-density correlation function, three-body correlation function and von
Neumann entropy estimator obtained by density matrix renormalization group
method. These exotic phases and phase transitions are expected to be observed
in the ultra-cold polar molecule experiments by properly tuning interaction
parameters, which is constructive to understand the physics of ubiquitous
insulating-superconducting phase transitions in condensed matter systems.
