Dynamics of one hole in the<i>t</i>-<i>J</i>model

Abstract

We calculated the spectral function of a hole in the t-J model using a numerical method on a 4\ifmmode\times\else\texttimes\fi{}4 lattice. A sharp quasiparticle peak is observed with an energy that is well approximated by \ensuremath{\Delta}E=-3.17+2.83${J}^{\ensuremath{\alpha}}$ (for 0.1\ensuremath{\le}J\ensuremath{\le}1.0, t=1) with \ensuremath{\alpha}=0.73\ifmmode\pm\else\textpm\fi{}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.