HOLE DYNAMICS IN A QUANTUM ANTIFERROMAGNET - EXTENSION OF THE RETRACEABLE-PATH APPROXIMATION

The one-hole spectral weight for two chains and two-dimensional lattic es is studied numerically using a method of analysis of the spectral f unction within the Lanczos iteration scheme: the Lanczos spectral deco ding method. This technique is applied to the t-J(z) model for J(z) -- > 0, directly on an infinite-size lattice. By a careful investigation of the first 13 Lanczos steps and the first 26 ones for the two-dimens ional and the two-chain cases, respectively, we find several interesti ng features of the one-hole spectral weight. A sharp incoherent peak w ith a clear momentum dispersion is identified, together with a second broad peak at higher energy. The spectral weight is finite up to the N agaoka energy where it vanishes in a nonanalytic way. Thus the lowest energy of one hole in a quantum antiferromagnet is degenerate with the Nagaoka energy in the thermodynamic limit.