000123893 001__ 123893 000123893 005__ 20230914083805.0 000123893 0247_ $$2doi$$a10.21468/SciPostPhysLectNotes.50 000123893 0248_ $$2sideral$$a132314 000123893 037__ $$aART-2022-132314 000123893 041__ $$aeng 000123893 100__ $$0(orcid)0000-0003-2995-6615$$aRomán-Roche, Juan 000123893 245__ $$aEffective theory for matter in non-perturbative cavity QED 000123893 260__ $$c2022 000123893 5060_ $$aAccess copy available to the general public$$fUnrestricted 000123893 5203_ $$aStarting from a general material system of N particles coupled to a cavity, we use a coherent-state path integral formulation to produce a effective theory for the material degrees of freedom. We tackle the effects of image charges, the A^2 term and a multimode arbitrary-geometry cavity. The resulting (non-local) action has the photonic degrees of freedom replaced by an effective position-dependent interaction between the particles. In the large-NN limit, we discuss how the theory can be cast into an effective Hamiltonian where the cavity induced interactions are made explicit. The theory is applicable, beyond cavity QED, to any system where bulk material is linearly coupled to a diagonalizable bosonic bath. We highlight the differences of the theory with other well-known methods and numerically study its finite-size scaling on the Dicke model. Finally, we showcase its descriptive power with three examples: photon condensation, the 2D free electron gas in a cavity and the modification of magnetic interactions between molecular spins; recovering, condensing and extending some recent results in the literature. 000123893 536__ $$9info:eu-repo/grantAgreement/ES/CSIC/PTI-001$$9info:eu-repo/grantAgreement/ES/DGA/E09-17R-Q-MAD$$9info:eu-repo/grantAgreement/EC/H2020/862893/EU/Molecular spin qudits offering new hope for quantum computing/FATMOLS$$9This project has received funding from the European Union’s Horizon 2020 research and innovation program under grant agreement No H2020 862893-FATMOLS$$9info:eu-repo/grantAgreement/ES/MICINN-AEI/PID2020-115221GB-C41 000123893 540__ $$9info:eu-repo/semantics/openAccess$$aby$$uhttp://creativecommons.org/licenses/by/3.0/es/ 000123893 594__ $$a9.1$$b2022 000123893 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion 000123893 700__ $$0(orcid)0000-0003-4478-1948$$aZueco, David 000123893 773__ $$g50 (2022), [32 pp.]$$pSciPost Phys. Lect. Notes$$tSciPost Physics Lecture Notes$$x2590-1990 000123893 8564_ $$s841305$$uhttps://zaguan.unizar.es/record/123893/files/texto_completo.pdf$$yVersión publicada 000123893 8564_ $$s1898289$$uhttps://zaguan.unizar.es/record/123893/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada 000123893 909CO $$ooai:zaguan.unizar.es:123893$$particulos$$pdriver 000123893 951__ $$a2023-09-13-15:23:49 000123893 980__ $$aARTICLE