Spin-Charge Decoupling and the One-Hole Green’s Function in a Quantum Antiferromagnet

The one-hole spectral weight for the two dimensional lattice is studied numerically using a recently developed technique, based on the Lanczos iteration scheme. This method is applied to the t — J z model for J z → 0, directly in the infinite size lattice. The presence of closed loop paths inhibit spin charge decoupling in two spatial dimensions although our calculation cannot rule out the existence of spin charge decoupling at long distance where the numerical calculation becomes prohibitive. Instead in the Bethe lattice case, for arbitrary coordination number, spin charge decoupling is satisfied at any distance-as in one dimension-due to the absence of closed loop paths.