Unified treatment of Fermi pockets and arcs scenarios for the cuprates: Sum rule consistent response functions of the pseudogap

Essential to understanding the cuprate pseudogap phase is a study of the charge (and spin) response functions, which we address here via a consistent approach to the Fermi arcs and the Fermi pockets scenario of Yang, Rice and Zhang (YRZ). The two schemes are demonstrated to be formally similar, and to share a common physics platform; we use this consolidation to address the inclusion of vertex corrections which have been omitted in YRZ applications. We show vertex corrections can be easily implemented in a fashion analytically consistent with sum rules and that they yield important contributions to most observables. A study of the charge ordering susceptibility of the YRZ scenario makes their simple physics evident: they represent the inclusion of charged bosonic, spin singlet degrees of freedom, and are found to lead to a double peak structure.