Properties of the non-linear Holstein polaron at finite doping and temperature

TL;DR

This study uses quantum Monte Carlo simulations to explore how small non-linear electron-phonon interactions affect quasiparticles, phonons, and charge-density wave tendencies in a 2D Holstein model, revealing significant impacts on effective coupling and phase behavior.

Contribution

It demonstrates the importance of non-linear electron-phonon interactions in modifying quasiparticle and phonon properties beyond linear models, with implications for real materials.

Findings

Positive non-linearity reduces e-ph coupling and suppresses CDW correlations.

Negative non-linearity enhances e-ph coupling and promotes CDW tendencies.

Quantitative effects of non-linearity cannot be fully captured by a simple linear renormalization.

Abstract

We use determinant quantum Monte Carlo to study the single particle properties of quasiparticles and phonons in a variant of the two-dimensional Holstein model that includes an additional non-linear electron-phonon (e-ph) interaction. We find that a small positive non-linear interaction reduces the effective coupling between the electrons and the lattice, suppresses charge-density wave (CDW) correlations, and hardens the effective phonon frequency. Conversely, a small negative non-linear interaction can enhance the e-ph coupling resulting in heavier quasiparticles, an increased tendency towards a CDW phase at all fillings, and a softened phonon frequency. An effective linear model with a renormalized interaction strength and phonon frequency can qualitatively capture this physics; however, the quantitative effects of the non-linearity on both the electronic and phononic degrees of freedom cannot be captured by such a model. These results are significant for typical non-linear coupling strengths found in real materials, indicating that non-linearity can have a significant influence on the physics of many e-ph coupled systems.