# Cavity QED of Strongly Correlated Electron Systems: A No-go Theorem for Photon Condensation

## TL;DR

This paper proves that gauge invariance prevents photon condensation in strongly correlated electron systems coupled to a cavity, and demonstrates through a microscopic model that certain phases do not support photon condensates.

## Contribution

It establishes a no-go theorem for photon condensation in non-relativistic many-body systems coupled to cavities and applies it to a specific extended Falicov-Kimball model.

## Key findings

- Gauge invariance forbids photon condensation in these systems.
- Insulating phases like ferroelectric and exciton condensates are unaffected by the cavity.
- The microscopic model confirms the no-go theorem's predictions.

## Abstract

In spite of decades of work it has remained unclear whether or not superradiant quantum phases, referred to here as photon condensates, can occur in equilibrium. In this Letter, we first show that when a non-relativistic quantum many-body system is coupled to a cavity field, gauge invariance forbids photon condensation. We then present a microscopic theory of the cavity quantum electrodynamics of an extended Falicov-Kimball model, showing that, in agreement with the general theorem, its insulating ferroelectric and exciton condensate phases are not altered by the cavity and do not support photon condensation.