Quantum Dynamics of the Hubbard-Holstein Model in Equilibrium and Non-Equilibrium: Application to Pump-Probe Phenomena

TL;DR

This paper investigates the quantum dynamics of the 2D Hubbard-Holstein model, revealing equilibrium spectral features and non-equilibrium phonon and spin oscillations post-pulse, with implications for high-temperature superconductor experiments.

Contribution

It provides a detailed analysis of the Hubbard-Holstein model's behavior in equilibrium and after ultrafast excitation, highlighting phonon and spin oscillations and their observability conditions.

Findings

Optical conductivity shows a 3-peak structure at strong coupling.

Phonon and spin subsystems oscillate with a period of approximately 80 fs after excitation.

Decay time of oscillations is about 150-200 fs, similar to charge relaxation time.

Abstract

The spectral response and physical features of the 2D Hubbard-Holstein model are calculated both in equilibrium at zero and low chemical dopings, and after an ultra short powerful light pulse, in undoped systems. At equilibrium and at strong charge-lattice couplings, the optical conductivity reveals a 3-peak structure in agreement with experimental observations. After an ultra short pulse and at nonzero electron-phonon interaction, phonon and spin subsystems oscillate with the phonon period $T_{ph} \approx 80$ fs. The decay time of the phonon oscillations is about 150-200 fs, similar to the relaxation time of the charge system. We propose a criterion for observing these oscillations in high $T_c$ compounds: the time span of the pump light pulse $\tau_{pump}$ has to be shorter than the phonon oscillation period $T_{ph}$.