Wick’s theorem for charged spin systems

We present a new Green’s-function approach to charged spin systems which preserves the local constraints prohibiting double occupancy. It is a systematic fermionic expansion and yields 1/(2z) as a control parameter for the Heisenberg model. For the t-J model the spin and hole Green’s functions are treated on an equal footing. In the Ising limit, the Brinkman-Rice approximation and a bandwidth ∼$J^z$ are recovered for, respectively, the incoherent and coherent hole motion. A new picture for the coherent hole propagation is obtained in the Heisenberg limit.