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

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.

Rotational Resonances and Regge Trajectories in Lightly Doped Antiferromagnets

“…For a better comparison of the overall spectral weight and shape, we added small overall energy shifts ∆ω separately for each m 4 and introduced broadening σ 1 = J of all higher excited states. Such broadening is expected to arise from couplings to magnon excitations in the AFM [38,69] which we neglect in our toy model calculation so far.…”