Dynamics of one hole in the t-J model

We calculated the spectral function of a hole in the t-J model using a numerical method on a 4×4 lattice. A sharp quasiparticle peak is observed with an energy that is well approximated by ΔE=-3.17+2.83$J^{\alpha }$ (for 0.1≤J≤1.0, t=1) with α=0.73±0.02. This result suggests that the picture of a hole attached to the origin by a string may be valid in the Heisenberg model. The rest of the spectrum is not completely incoherent but it has a nontrivial structure, stemming from the excited states of the string. The bandwidth of the quasiparticle is discussed. Results for the Ising model are also presented.