Hole dynamics in a quantum antiferromagnet: Extension of the retraceable-path approximation

The one-hole spectral weight for two chains and two-dimensional lattices is studied numerically using a method of analysis of the spectral function within the Lanczos iteration scheme: the Lanczos spectral decoding 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-dimensional and the two-chain cases, respectively, we find several interesting features of the one-hole spectral weight. A sharp incoherent peak with a clear momentum dispersion is identified, together with a second broad peak at higher energy. The spectral weight is finite up to the Nagaoka 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.