Density-matrix renormalization group study of third harmonic generation in one-dimensional Mott insulator coupled with phonon

TL;DR

This study investigates the third harmonic generation in a one-dimensional Mott insulator with phonons, revealing how electron-phonon interactions influence non-linear optical responses and spin excitations using advanced numerical methods.

Contribution

It provides the first detailed analysis of THG in a Mott insulator coupled with phonons, highlighting the role of electron-phonon interactions and spin excitations.

Findings

Electron-phonon interaction enhances THG intensity under certain conditions.

THG spectrum can detect spin excitations even without electron-phonon coupling.

Electron-phonon coupling slightly increases low-energy THG weight without creating new peaks.

Abstract

We examine the third-order non-linear optical response of a one-dimensional Mott insulator coupled with phonons. The Mott insulator is described by an extended Hubbard-Holstein model. The third harmonic generation (THG) of the model is calculated by dynamical density-matrix renormalization group. We find that the electron-phonon interaction enhances the intensity of THG if the on-site Coulomb interaction is comparable to the band width, but the enhancement is small for a realistic parameter value of a typical Mott insulator Sr$_2$CuO$_3$. The low-energy spin excitation does not contribute to the optical response if the electron-phonon coupling is neglected. We find that the THG spectrum can detect the spin excitations even for no electron-phonon coupling. The introduction of the electron-phonon coupling leads to a slight increase of low-energy weight in THG without peak structure through phonon-assisted spin excitation. To fully understand the phonon-assisted spin excitation, we additionally calculate the linear susceptibility of a doped Hubbard-Holstein model, showing a spectral distribution different from that at half filling.