Abstract
Using the slave boson method for the 1-band Hubbard model, we derive an effective Hamiltonian in terms of charge and spin variables. For large values of the Hubbard U we recover the standard t-J model. For smaller values of U the range of interaction between the spin and charge variables is increased. We also consider the effect of an onsite electron-phonon interaction and show that the effect of integrating the double occupancy and the integration of phonons is in general not additive.
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