Competing phases in the cuprates: Charge vs spin order

We have investigated magnetic and charge instabilities of the cuprates within the Gutzwiller approximation RPA (GA+RPA). Interestingly, in GA the dressed Hubbard U is not a single parameter, but has different forms in the spin and charge responses, with distinct doping dependencies. While there are a number of competing magnetic instabilities for hole-doped cuprates, we fail to find any purely electronic charge density waves. The dominant magnetic instabilities are associated with 'double nesting', and the phase diagrams are material dependent, with LSCO differing from other cuprates.