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