Functional Renormalization Group Approach to Circuit Quantum Electrodynamics

TL;DR

This paper introduces a nonperturbative functional renormalization group method to analyze superconducting circuits in circuit QED, revealing new phase behaviors and the limitations of traditional models due to strong parameter renormalizations.

Contribution

It develops a novel nonperturbative framework for cQED systems, capturing effects missed by perturbative approaches and explaining breakdowns of existing effective models.

Findings

Nonperturbative effects cause breakdown of effective models.

Strong renormalizations significantly alter low-energy physics.

New phase diagrams emerge from the analysis.

Abstract

A nonperturbative approach is developed to analyze superconducting circuits coupled to quantized electromagnetic 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 breakdown of the supposedly effective descriptions, such as the spin-boson and boundary sine-Gordon models, and lead to qualitatively new 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.