Hole in the two-dimensional Ising antiferromagnet: Origin of the incoherent spectrum

We develop a self-avoiding walks approximation and use it to calculate the spectral function of a single hole introduced into a two-dimensional square lattice Ising antiferromagnet. The local spectral function obtained qualitatively agrees with the exact diagonalization 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.

Automated summary

This study introduces a self-avoiding walks approximation to calculate the spectral function of a single hole in a two-dimensional square lattice Ising antiferromagnet. The obtained local spectral function qualitatively agrees with exact diagonalization results and is largely incoherent. The incoherent spectrum on the square lattice is not triggered by Trugman loops, but originates from interactions between magnons created along the tangential paths of the moving hole, warping the linear potential.