Polaron in the t-J Models with Three-Site Terms: the SU(2) and the Ising Cases

We compare the role of the three-site terms added to the t-J models in the SU(2) and the Ising cases in the extremely low doping regime, i.e. when a single hole added to the strongly interacting half-filled system becomes a polaron. We show that in the realistic Ising case the three-site terms play a vital role in the polaron movement and should never be neglected unlike in the SU(2) case.