Spectral properties of the t-J model in the presence of hole-phonon interaction

We examine the effects of electron-phonon interaction on the dynamics of the charge carriers doped in two-dimensional (2D) Heisenberg antiferromagnet. The t-J model Hamiltonian with a Frohlich term which couples the holes to a dispersionless (optical) phonon mode is considered for low doping concentration. The evolution of the spectral density function, the density of states, and the momentum distribution function of the holes with an increase of the hole-phonon coupling constant g is studied numerically. As the coupling to a phonon mode increases the quasiparticle spectral weight decreases and a ''phonon satellite'' feature close to the quasiparticle peak becomes more pronounced. Furthermore, strong electron-phonon coupling smears the multimagnon resonances (''string states'') in the incoherent part of the spectral function. The jump in the momentum distribution function at the Fermi surface is reduced without changing the hole pocket volume, thereby providing a numerical verification of Luttinger theorem for this strongly interacting system. The vertex corrections due to electron-phonon interaction are negligible in spite of the fact that the ratio of the phonon frequency to the effective bandwidth is not small.