Hole motion in the Ising antiferromagnet: an application of the recursion method

TL;DR

This paper investigates hole dynamics in the Ising antiferromagnet using the recursion method, analyzing the Green's function and wavefunction across different interaction strengths, and considering transverse interactions for deeper insight.

Contribution

It applies the recursion method to study hole motion in the Ising antiferromagnet, extending understanding beyond the self-consistent Born approximation.

Findings

Derived the hole's Green's function for various t/J_z ratios

Analyzed the wavefunction of the hole in the antiferromagnetic background

Assessed the impact of small transverse interactions on hole dynamics

Abstract

We study hole motion in the Ising antiferromagnet using the recursion method. Using the retraceable path approximation we find the hole's Green's function as well as its wavefunction for arbitrary values of $t/J_z$. The effect of small transverse interaction also is taken into account. Our results provide some additional insight into the self-consistent Born approximation.