Electron-phonon interaction in undoped cuprates: Sum rules, vertex corrections and the self-consistent Born approximation

Having the undoped cuprates in mind, we study an undoped t-J model with electron-phonon coupling using the self-consistent Born approximation (SCBA). While the SCBA has been shown to be quite accurate for a pure t-J model, we find it less accurate when electron-phonon coupling is included. Exact diagonalization of the underlying boson-holon model shows that deviations are mainly due to the neglect of vertex corrections for small J/t and due to the introduction of the boson-holon model for large J/t. A very simple approximation to the electron self-energy gives a rather accurate effective mass allowing us to study factors influencing the electron-phonon interaction