Functional-renormalization-group approach to circuit quantum electrodynamics

A nonperturbative approach is developed to analyze superconducting circuits coupled to quantized electro-magnetic continuum within the framework of the functional renormalization group. The formalism allows us to determine complete physical pictures of equilibrium properties in the circuit quantum electrodynamics (cQED) architectures with high-impedance waveguides, which have recently become accessible in experiments. We point out that nonperturbative effects can trigger a breakdown of the supposedly effective descriptions, such as the spin-boson and boundary sine-Gordon models, and lead to qualitatively unique phase diagrams. The origin of the failure of conventional understandings is traced to strong renormalizations of circuit parameters at low-energy scales. Our results indicate that a nonperturbative analysis is essential for a comprehensive understanding of cQED platforms consisting of superconducting circuits and long high-impedance transmission lines.