Renormalization Group Flow of the Jaynes-Cummings Model

The Jaynes-Cummings model is a cornerstone of light-matter interactions. While finite, the model provides an illustrative example of renormalization in perturbation theory. We show, however, that exact renormalization reveals a rich nonperturbative structure, and that the model provides a physical example of a theory with a chaotic coupling trajectory and multivalued β function. We also construct an exact Wilsonian-like renormalization group flow for the effective scattering matrix, and show how multivalued features arise in the flow. Our results shed light on nonperturbative aspects of renormalization and on the structure of the Jaynes-Cummings model itself.