Lattice and surface effects in the out-of-equilibrium dynamics of the Hubbard model

TL;DR

This paper investigates the out-of-equilibrium dynamics of the Hubbard-Holstein model using the time-dependent Gutzwiller approximation, revealing a mean-field dynamical transition and surface energy trapping influenced by electron-phonon interactions.

Contribution

It introduces a detailed analysis of out-of-equilibrium behavior in correlated electron systems with phonons, highlighting a dynamical transition and surface energy trapping phenomena.

Findings

Evidence of a mean-field dynamical transition with lattice distortion

Surface energy trapping occurs for large deviations from equilibrium

Electron-phonon coupling enhances surface energy trapping

Abstract

We study, by means of the time-dependent Gutzwiller approximation, the out of equilibrium dynamics of a half-filled Hubbard-Holstein model of correlated electrons interacting with local phonons. Inspired by pump-probe experiments, where intense light pulses selectively induce optical excitations that trigger a transient out-of-equilibrium dynamics, here we inject energy in the Hubbard bands by a non-equilibrium population of empty and doubly-occupied sites. We first consider the case of a global perturbation, acting over the whole sample, and find evidence of a mean-field dynamical transition where the lattice gets strongly distorted above a certain energy threshold, despite the weak strength of the electron-phonon coupling by comparison with the Hubbard repulsion. Next, we address a slab geometry for a correlated heterostructure and study the relaxation dynamics across the system when the perturbation acts locally on the first layer. While for weak deviations from equilibrium the excited surface is able to relax by transferring its excess energy to the bulk, for large deviations the excess energy stays instead concentrated into the surface layer. This self-trapping occurs both in the absence as well as in the presence of electron-phonon coupling. Phonons actually enforce the trapping by distorting at the surface.