Static overscreening and nonlinear response in the Hubbard model

We investigate the static charge response for the Hubbard model. Using the slave-boson method in the saddle-point approximation we calculate the charge susceptibility. We find that the random phase approximation (RPA) works quite well close to half filling, breaking, of course, down close to the Mott transition. Away from half filling RPA is much less reliable: Already for very small values of the Hubbard interaction U, the linear response becomes much more efficient than RPA, eventually leading to overscreening already beyond quite moderate values of U. To understand this behavior we give a simple argument, which implies that the response to an external perturbation at large U should actually be strongly nonlinear. This prediction is confirmed by the results of exact diagonalization.