Correlations at a quantum phase transition in interacting Bose systems

We have investigated the correlation functions of interacting bosons at the generic superfluid-insulator transition, a prototypical quantum phase transition, in two dimensions in the spherical limit. Unexpectedly the spatial correlation functions show non-power-law behavior consisting of two parts: short-range correlation due to the particle-hole pair excitations and long-range off-diagonal order due to the single-particle condensation. The temporal correlation functions, on the other hand, show power-law behavior.