Hole in the 2D Ising Antiferromagnet: Origin of the Incoherent Spectrum

TL;DR

This paper introduces a self-avoiding walks approximation to analyze the spectral function of a hole in a 2D Ising antiferromagnet, revealing the origin of incoherent spectra due to magnon interactions.

Contribution

It presents a novel approximation method that explains the incoherent spectral features in the 2D Ising antiferromagnet, contrasting with Bethe lattice results.

Findings

Spectral function is largely incoherent and agrees qualitatively with exact diagonalization.

Incoherence is caused by magnon interactions, not Trugman loops.

The spectrum differs from Bethe lattice results, lacking well-separated quasiparticle peaks.

Abstract

We develop a "self-avoiding walks" approximation and use it to calculate the spectral function of a single hole introduced into the 2D square lattice Ising antiferromagnet. The obtained local spectral function qualitatively agrees with the exact diagonalisation result and is largely incoherent. Such a result stays in contrast with the spectrum obtained on a Bethe lattice, which consists of the well-separated quasiparticle-like peaks and stems from the motion of a hole in an effective linear potential. We determine that this onset of the incoherent spectrum on a square lattice (i) is not triggered by the so-called Trugman loops but (ii) originates in the warping of the linear potential by the interactions between magnons created along the tangential paths of the moving hole.