Exotic Phases of Hard-core Bosons with Correlated Hopping

We investigate the interplay of correlated hopping and repulsive interactions for hard-core bosons on a square lattice using quantum Monte Carlo simulations. The first part of this contribution is on a remarkable low-density pairing phase. 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 nearest-neighbor repulsion suppresses phase separation, leading to a low-density pairing phase with no single particle Bose-Einstein condensation but long-range two-particle correlations, signalling a condensation of pairs. The second part of this contribution targets at the physics at higher densities. Here, the most important question is the possible existence of a supersolid phase in such a model with correlated hopping. \newline [1] K.P. Schmidt, J. Dorier, A. Laeuchli, and F. Mila, Phys. Rev. B 74, 174508 (2006).