## Incompressible phase in lattice systems of interacting bosons

C. Borgs, R. Kotecky and D. Ueltschi

unpublished (1997)Phase diagrams for a class of boson lattice models with small hopping and at low temperatures are rigorously described. We show that incompressibility is a general property of systems with strong interactions and conservation of the total particle number. More precisely, we prove that the density (as a function of the pressure) exhibits plateaux at zero temperature. As an application, we investigate the Bose-Hubbard model with nearest and next nearest neighbour interactions and show that it exhibits long-range order. For magnetic systems, we show that the zero temperature susceptibility with respect to the magnetic field in the z-direction vanishes, if the Hamiltonian commutes with the z-component of the total spin.