Dynamical mean field theory of optical third harmonic generation

TL;DR

This paper develops a DMFT-based approach to calculate third harmonic generation spectra in the Hubbard model, revealing a universal scaling behavior across Mott insulators.

Contribution

It formulates the THG within DMFT, simplifying calculations by eliminating vertex corrections and uncovering a universal scaling function for Mott insulators.

Findings

THG spectra can be computed via a convolution in DMFT.

Vertex corrections are zero in the large dimension limit.

A universal scaling function describes THG in Mott insulators.

Abstract

We formulate the third harmonic generation (THG) within the dynamical mean field theory (DMFT) approximation of the Hubbard model. In the limit of large dimensions, where DMFT becomes exact, the vertex corrections to current vertices are identically zero, and hence the calculation of the THG spectrum reduces to a time-ordered convolution, followd by appropriate analytic continuuation. We present the typical THG spectrum of the Hubbard model obtained by this method. Within our DMFT calculation, we observe a nontrivial approximate {\em scaling} function describing the THG spectra in all Mott insulators, independent of the gap magnitude.