A non-perturbative no-go theorem for photon condensation in approximate models

TL;DR

This paper proves a fundamental no-go theorem that rules out both first- and second-order photon condensation phase transitions in approximate models that are gauge-invariant and do not include magnetic field coupling.

Contribution

It establishes a general no-go theorem applicable to truncated, gauge-invariant models, preventing superradiant phase transitions without magnetic field interaction.

Findings

No superradiant phase transition occurs in gauge-invariant models without magnetic coupling.

The theorem applies to lattice electrons and multi-level systems.

First- and second-order phase transitions are both forbidden under these conditions.

Abstract

Equilibrium phase transitions between a normal and a photon condensate state (also known as superradiant phase transitions) are a highly debated research topic, where proposals for their occurrence and no-go theorems have chased each other for the past four decades. Recent no-go theorems have demonstrated that gauge invariance forbids second-order phase transitions to a photon condensate state when the cavity-photon mode is assumed to be {\it spatially uniform}. However, it has been theoretically predicted that a collection of three-level systems coupled to light can display a first-order phase transition to a photon condensate state. %{It has also been recently shown that truncation of the Hilbert space of the matter system can affect the gauge invariance of the theory. However, it is always possible to obtain approximate Hamiltonians obeying the gauge principle in the truncated Hilbert space.} Here, we demonstrate a general no-go theorem valid also for truncated, gauge-invariant models which forbid first-order as well as second-order superradiant phase transitions in the absence of a coupling with a magnetic field. In particular, we explicitly consider the cases of interacting electrons in a lattice and $M$-level systems.