Dynamical t/U Expansion Theory of a Doped Hubbard Model

In this work, we construct a new U(1) slave representation for the single band Hubbard model in the large-U limit. By employing a dynamic Green's function method for the slave spins, we formulate a dynamic t/U expansion for the Hubbard model which reduces the model to a t-J-type low energy effective theory for the spinons and an XXZ-type effective theory for the slave spins. This new approach recovers our previous slave rotor results for the Mott insulating state at half-filling, and is more amenable to describe the strong correlation effects in the finite doping regime. By solving the slave spin theory at the mean field level for finite doping, we find that the superexchange interaction strength J, as well as the effective spinon hopping amplitude, develops doping dependence. More interestingly, pairing-type interaction in the dynamic Green's function shows up, which solely stems from quantum fluctuations of the doping driven Mott-insulator-to-metal transition.