# Reduced Density-Matrix Approach to Strong Matter-Photon Interaction

## TL;DR

This paper introduces a non-perturbative, first-principles reduced density-matrix approach to model strongly coupled matter-photon systems, enabling accurate analysis of complex electronic-photon interactions.

## Contribution

It develops a novel higher-dimensional auxiliary system to map coupled fermion-boson systems into a dressed fermionic problem, facilitating the use of conventional density-matrix functional theory.

## Key findings

- Simple density-matrix approximations are accurate across coupling regimes.
- The influence of the photon field depends on electronic structure details.
- Method is applicable to complex systems beyond exact calculation capabilities.

## Abstract

We present a first-principles approach to electronic many-body systems strongly coupled to cavity modes in terms of matter-photon one-body reduced density matrices. The theory is fundamentally non-perturbative and thus captures not only the effects of correlated electronic systems but accounts also for strong interactions between matter and photon degrees of freedom. We do so by introducing a higher-dimensional auxiliary system that maps the coupled fermion-boson system to a dressed fermionic problem. This reformulation allows us to overcome many fundamental challenges of density-matrix theory in the context of coupled fermion-boson systems and we can employ conventional reduced density-matrix functional theory developed for purely fermionic systems. We provide results for one-dimensional model systems in real space and show that simple density-matrix approximations are accurate from the weak to the deep-strong coupling regime. This justifies the application of our method to systems that are too complex for exact calculations and we present first results, which show that the influence of the photon field depends sensitively on the details of the electronic structure.