# Multi-band non-equilibrium GW+EDMFT formalism for correlated insulators

## TL;DR

This paper develops a nonequilibrium multi-band GW+EDMFT formalism to study charge-transfer insulators under photo-excitation, revealing significant spectral and optical property changes driven by non-local charge fluctuations.

## Contribution

It introduces a detailed derivation of a nonequilibrium multi-band GW+EDMFT framework and applies it to analyze photo-induced dynamics in cuprate-like insulators.

## Key findings

- Charge-transfer gap is strongly renormalized after photo-excitation.
- Momentum-dependent broadening observed in the upper Hubbard band.
- Optical conductivity indicates gap renormalization proportional to photo-doping.

## Abstract

We study the dynamics of charge-transfer insulators after a photo-excitation using the three-band Emery model which is relevant for the description of cuprate superconductors. We provide a detailed derivation of the nonequilibrium extension of the multi-band GW+EDMFT formalism and the corresponding downfolding procedure. The Peierls construction of the electron-light coupling is generalized to the multi-band case resulting in a gauge invariant combination of the Peierls intra-band acceleration and dipolar intra-band transitions. We apply the formalism to the study of momentum-dependent (inverse) photo-emission spectra and optical conductivities. The time-resolved spectral function shows a strong renormalization of the charge-transfer gap and a substantial broadening of some of the bands. While the upper Hubbard band exhibits a momentum-dependent broadening, an almost rigid band shift is observed for the ligand bands. The inverse photo-emission spectrum reveals that the inclusion of the non-local and inter-band charge fluctuations lead to a very fast relaxation of holes into the lower Hubbard band. Consistent with the changes in the spectral function, the optical conductivity shows a renormalization of the charge-transfer gap, which is proportional to the photo-doping. The details of the photo-induced changes strongly depend on the dipolar matrix elements, which calls for an ab-initio determination of these parameters.