In metals containing magnetic impurities, conduction electrons screen the magnetic impurities and induce the Kondo effect, i.e., the enhancement of the electrical resistance at low temperatures. Motivated by recent advances in manipulating quantum materials by cavity confinement, we study how the ultrastrong light-matter coupling can affect the Kondo effect. We show that the ultrastrong coupling can enhance the Kondo temperature and give rise to several notable phenomena, including universal scalings of the cavity-modified Kondo effect, the photon occupation number, and the entanglement entropy between the cavity and electrons. The origin of the cavity enhancement can be understood from the mass renormalization due to the cavity-mediated nonlocal electron-electron interaction, which is akin to the polaronic mass enhancement. We combine the unitary transformations and the Gaussian variational states to analyze the quantum impurity system confined in the cavity. Our nonperturbative framework can be applied to a variety of quantum impurity problems influenced by structured quantum electromagnetic environment.

14 pages, 4 figures