Density fluctuations of a hard-core Bose gas in a one-dimensional lattice

For a hard-core Bose gas on a one-dimensional lattice we find characteristic oscillations in the density-density correlation function. Their wavelength diverges as the system undergoes a continuous transition from an incommensurate to a Mott insulating phase. The associated static structure factor vanishes as the Mott insulating phase is approached. The qualitative picture is unchanged when a weak confinig potential is applied to the system.