Based on worm-type Monte Carlo method, we simulate the two-dimensional Bose-Hubbard model and the classical (2+1)-dimensional J-current model near the critical point.We determine the spectral functions for the magnitude squared of the order parameter, revealing a low-frequency resonance, for all the superfluid, Mott insulator, and normal liquid phases.The counterintuitive resonance feature in the latter two phases calls for deeper theoretical understanding.Moreover, we precisely determine the universal conductivity on the quantum critical plateau and the shape of the universal function as Matsubara frequency.The precision is high enough for a comparison with the prediction from the AdS/CFT correspondence theory.