  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.
