Spectral function of a hole in thet-Jmodel

We give numerical solutions, on finite but large-size square lattices, of the equation for the single-hole Green’s function obtained by the self-consistent approach of Schmitt-Rink et al. and Kane et al. The spectral function of the hole in a quantum antiferromagnet shows that most features describing the hole motion are in close agreement with the results of the exact diagonalization on the $4^2$ lattice in the region of J/t≤0.2. Our results obtained on sufficiently large-size lattices suggest that certain important features of the spectral function survive in the thermodynamic limit while others change due to finite-size effects. We find that the leading nonzero vertex correction is given by a two-loop diagram, which has a small contribution.