## Effective theory for matter in non-perturbative cavity QED

Juan Román-Roche, David Zueco

SciPost Phys. Lect. Notes 50 (2022) · published 10 May 2022

- doi: 10.21468/SciPostPhysLectNotes.50
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### Abstract

Starting from a general material system of $N$ particles coupled to a cavity, we use a coherent-state path integral formulation to produce a non-perturbative effective theory for the material degrees of freedom. We tackle the effects of image charges, the $A^2$ term and a multimode arbitrary-geometry cavity. The resulting (non-local) action has the photonic degrees of freedom replaced by an effective position-dependent interaction between the particles. In the large-$N$ limit, we discuss how the theory can be cast into an effective Hamiltonian where the cavity induced interactions are made explicit. The theory is applicable, beyond cavity QED, to any system where bulk material is linearly coupled to a diagonalizable bosonic bath. We highlight the differences of the theory with other well-known methods and numerically study its finite-size scaling on the Dicke model. Finally, we showcase its descriptive power with three examples: photon condensation, the 2D free electron gas in a cavity and the modification of magnetic interactions between molecular spins; recovering, condensing and extending some recent results in the literature.

### Cited by 13

### Authors / Affiliation: mappings to Contributors and Organizations

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^{1}Juan Román-Roche, -
^{1}David Zueco

- Consejo Superior de Investigaciones Científicas / Spanish National Research Council [CSIC]
- European Commission [EC]
- Gobierno de Aragón
- Ministerio de Economía y Competitividad (MINECO) (through Organization: Ministerio de Economía, Industria y Competitividad / Ministry of Economy, Industry and Competitiveness [MINECO])