A non-perturbative no-go theorem for photon condensation in approximate models
NEST, Scuola Normale Superiore, 56126, Pisa, Italy
2 Istituto Italiano di Tecnologia, Graphene Labs, Via Morego 30, 16163, Genoa, Italy
3 ICFO - Institut de Ciencies Fotoniques, Mediterranean Technology Park, 08860, Castelldefels, Barcelona, Spain
4 Dipartimento di Fisica e Astronomia “Ettore Majorana”, Università di Catania, Via S. Sofia 64, 95123, Catania, Italy
5 INFN, Sez. Catania, 95123, Catania, Italy
6 Dipartimento di Scienze Matematiche e Informatiche, Scienze Fisiche e Scienze della Terra, Università di Messina, 98166, Messina, Italy
7 Dipartimento di Fisica dell’Università di Pisa, Largo Bruno Pontecorvo 3, 56127, Pisa, Italy
8 School of Physics and Astronomy, University of Manchester, Oxford Road, M13 9PL, Manchester, UK
Accepted: 5 December 2022
Published online: 16 December 2022
Equilibrium phase transitions between a normal and a photon condensate state (also known as super-radiant 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 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. Here, we demonstrate a general no-go theorem valid also for truncated, gauge-invariant models which forbids first-order as well as second-order super-radiant 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.
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