Gutzwiller Charge and Magnetic Phase Diagrams of Cuprates*

We extend our previous analysis of the magnetic phase diagram of the cuprates to look for charge instabilities, either purely electronic or involving electron-phonon coupling, employing Gutzwiller approximation GA+RPA calculations of the Hubbard model. In the absence of phonons we find an overscreening instability for large doping at $(\pi ,\pi)$. In the presence of electron-phonon coupling, we find a rich response to Fermi surface nesting, very similar to the magnetic case, and in this case the instability criterion can be formulated as a generalized Stoner criterion. In the hole-doping regime, where evidence exists for a nonmagnetic (stripe) pseudogap, we find competing instabilities. Since the same susceptibility peaks are present for both spin and charge excitations, differences in preferred $q$-vectors arise from the $q$-dependence of the interaction $U_{eff,q}$.