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

TL;DR

This study investigates how electron-phonon interactions influence the spectral properties of holes in the 2D t-J model, revealing effects on quasiparticle weight, spectral features, and Fermi surface characteristics.

Contribution

It provides a numerical analysis of the spectral evolution in the t-J model with hole-phonon coupling, highlighting the minimal impact of vertex corrections and confirming Luttinger's theorem.

Findings

Decreased quasiparticle spectral weight with increased phonon coupling

Emergence of phonon satellite features near quasiparticle peaks

Preservation of Fermi surface volume despite spectral smearing

Abstract

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 Fr\"ohlich 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 quasi-particle peak becomes more pronounced. Furthermore, strong electron-phonon coupling smears the multi-magnon 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.