Analytical Results for a Hole in an Antiferromagnet

TL;DR

This paper analytically derives the Green's function for a hole in an antiferromagnet, showing finite quasiparticle weight in higher dimensions and suggesting polaronic hole motion with a specific bandwidth dependence.

Contribution

It provides an analytical solution for the hole Green's function in antiferromagnets, clarifying infrared divergence issues and the nature of hole motion.

Findings

Infrared divergence is eliminated in two or more dimensions.

Quasiparticle weight remains finite in higher dimensions.

Hole bandwidth is proportional to $t/J imes ext{exp}[-c (t/J)^2]$.

Abstract

The Green's function for a hole moving in an antiferromagnet is derived analytically in the long-wavelength limit. We find that the infrared divergence is eliminated in two and higher dimensions so that the quasiparticle weight is finite. Our results also suggest that the hole motion is polaronic in nature with a bandwidth proportional to $t/J \exp [-c (t/J)^2] $ ($c$ is a constant). The connection of the long-wavelength approximation to the first-order approximation in the cumulant expansion is also clarified.