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

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.

12 pages, 1 figure

References in corpus (10)

• Is there a no-go theorem for superradiant quantum phase transitions in cavity and circuit QED ?
• Intermolecular interactions in optical cavities: an ab initio QED study
• Theory of Photon Condensation in a Spatially-Varying Electromagnetic Field
• Adequacy of the Dicke model in cavity QED: a counter-"no-go" statement
• Drude weight, cyclotron resonance, and the Dicke model of graphene cavity QED
• Stability of polarizable materials against superradiant phase transition
• Effective theory of lattice electrons strongly coupled to quantum electromagnetic fields
• Effective theory for matter in non-perturbative cavity QED
• Signatures of the $A^2$ term in ultrastrongly-coupled oscillators
• Vacuum anomalous Hall effect in gyrotropic cavity

Cited by in corpus (15)

• Switchable Superradiant Phase Transition with Kerr Magnons
• First-order photon condensation in magnetic cavities: A two-leg ladder model
• Topological protection of Majorana polaritons in a cavity
• Local Fluctuations in Cavity Control of Ferroelectricity
• Photon condensation, Van Vleck paramagnetism, and chiral cavities
• Theory of fractional quantum Hall liquids coupled to quantum light and emergent graviton-polaritons
• Superradiant phase transitions in the quantum Rabi model: Overcoming the no-go theorem through anisotropy
• Phase Transitions in the Anisotropic Dicke-Stark Model with $A$-square terms
• Hidden excitonic quantum states with broken time-reversal symmetry
• Quantum Phase Transitions in Many-Dipole Light-Matter Systems
• Quantum Electrodynamics of graphene Landau levels in a deep-subwavelength hyperbolic phonon polariton cavity
• Light-matter interactions in the vacuum of ultra-strongly coupled systems
• Quantum phase diagrams of Dicke-Ising models by a wormhole algorithm
• Ultrafast dynamics of quantum matter driven by time-energy entangled photons
• Superradiant Quantum Phase Transition in Open Systems: System-Bath Interaction at the Critical Point