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 $U_{eff,q}$.