  We investigate the consequences of correlated hopping on the ground state
properties of hard-core bosons on a square lattice as revealed by extensive
exact diagonalizations and quantum Monte Carlo simulations. While for non
interacting hard-core bosons the effective attraction induced by the correlated
hopping leads to phase separation at low density, we show that a modest
nearest-neighbor repulsion suppresses phase separation, leading to a remarkable
low-density pairing phase with no single particle Bose-Einstein condensation
but long-range two-particle correlations, signaling a condensation of pairs. We
also explain why the unusual properties of the pairing phase are a real
challenge for standard one-worm quantum Monte Carlo simulations.
