Interaction and doping dependence of optical spectral weight of the two-dimensional Hubbard model

We calculate the total and low-frequency spectral weight of the optical conductivity of the two-dimensional Hubbard model for various values of the interaction strength and carrier concentration. In some limits we obtain exact results and bounds. For general parameter values we obtain estimates using the variational Monte Carlo technique. We show that our results disagree with those obtained by exact diagonalization of small systems, and argue that the latter are less accurate because of finite-size effects.