Finite-temperature spectral function of a hole in a quantum antiferromagnet and the role of phonons

Abstract

We study thermal broadening of the hole spectral function of the two-dimensional $t\text{\ensuremath{-}}J$ model (and its extensions) within the noncrossing approximation (NCA) with and without the contribution of optical phonons. We find that phonons at finite temperature broaden the lowest energy quasiparticle peak, however, the string excitations survive even for relatively strong electron-phonon coupling. Experimental angle-resolved photoemission spectroscopy (ARPES) results compare well with our calculations at finite temperature when we use strong electron-phonon coupling without any ad hoc broadening. In addition, we have studied the role of vertex corrections and we find that their contribution allows us to achieve the same overall agreement with the ARPES experimental results but using smaller values for the electron-phonon coupling $(\ensuremath{\gamma}\ensuremath{\sim}0.5)$ than that required $(\ensuremath{\gamma}\ensuremath{\sim}1)$ when restricting ourselves within NCA.