Phase separation in one-dimensional hard-core boson system with two- and three-body interactions

We investigate the ground state phase diagram of hard-core boson system with repulsive two-body and attractive three-body interactions in one-dimensional optical lattice. When these two interactions are comparable and increasing the hopping rate, physically intuitive analysis indicates that there exists a phase separation region 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 phases and phase transitions are expected to be observed in the ultra-cold polar molecule experiments by properly tuning interaction parameters as suggested in Methods by Büchler et al. [Nat. Phys. 3, 726 (2007)], which is constructive to understand the physics of ubiquitous insulating-superconducting phase transitions in condensed matter systems.