Hole dynamics in a quantum antiferromagnet beyond the retraceable path approximation

TL;DR

This paper introduces a new numerical method to analyze hole dynamics in quantum antiferromagnets, revealing detailed spectral features and the degeneracy of the lowest energy state with the Nagaoka energy.

Contribution

A novel Lanczos spectra decoding method applied to the $t-J_z$ model, providing new insights into the spectral weight and energy degeneracies in infinite lattices.

Findings

Identification of a sharp incoherent peak with momentum dispersion

Spectral weight remains finite up to the Nagaoka energy

Lowest energy of one hole is degenerate with Nagaoka energy in the thermodynamic limit

Abstract

The one-hole spectral weight for two chains and two dimensional lattices is studied numerically using a new method of analysis of the spectral function within the Lanczos iteration scheme: the Lanczos spectra decoding method. This technique is applied to the $t-J_z$ model for $J_z \to 0$, directly in the 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 get several new 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 non-analytic way. Thus the lowest energy of one hole in a quantum antiferromagnet is degenerate with the Nagaoka energy in the thermodynamic limit.