Exact correlation functions in the cuprate pseudogap phase: Combined effects of charge order and pairing

There is a multiplicity of charge-ordered, pairing-based, or pair density wave theories of the cuprate pseudogap, albeit arising from different microscopic mechanisms. For mean-field schemes (of which there are many) we demonstrate here that they have precise implications for two-body physics in the same way that they are able to address the one-body physics of photoemission spectroscopy. This follows because the full vertex can be obtained exactly from the Ward-Takahashi identity. As an illustration, we present the spin response functions, finding that a recently proposed pair density wave (Amperean pairing) scheme is readily distinguishable from other related scenarios.