Dressing due to correlations strongly reduces the effect of electron-phonon coupling

TL;DR

This paper demonstrates that correlations in strongly correlated systems significantly weaken the effective electron-phonon coupling, leading to minimal impact on quasiparticle mass despite moderate to strong bare coupling.

Contribution

It introduces a model showing how correlations dress quasiparticles, strongly reducing their effective electron-phonon interaction compared to bare carriers.

Findings

Correlation dressing weakens electron-phonon coupling effects.

Quasiparticle effective mass increases minimally despite strong bare coupling.

The suppression of phonon effects is expected in strongly correlated systems.

Abstract

We investigate the difference between the coupling of a bare carrier to phonons versus the coupling of a correlations-dressed quasiparticle to phonons, and show that latter may be weak even if the former is strong. Specifically, we analyze the effect of the hole-phonon coupling on the dispersion of the quasiparticle that forms when a single hole is doped into a cuprate layer. To model this, we start from the three-band Emery model supplemented by the Peierls modulation of the $p$-$d$ and $p$-$p$ hoppings due to the motion of O ions. We then project onto the strongly correlated $U_{dd}\rightarrow \infty$ limit where charge fluctuations are frozen on the Cu site. The resulting effective Hamiltonian describes the motion of a doped hole on the O sublattice, and its interactions with Cu spins and O phonons. We show that even though the hole-phonon coupling is moderate to strong, it leads to only a very minor increase of the quasiparticle's effective mass as compared to its mass in the absence of coupling to phonons, consistent with a weak coupling to phonons of the correlations-dressed quasiparticle. We explain the reasons for this suppression, revealing why it is expected to happen in any systems with strong correlations.