Limitations of Caldeira-Leggett model for description of phase transitions in superconducting circuits

Accurate modeling of system-bath interactions in quantum systems is a challenge of intrinsic complexity. Here, the authors show that seemingly minute changes in the model approximations heavily impact the renormalization group flow and phase diagram of resistive superconducting circuits. A modified Caldeira-Leggett model is presented with four instead of two control parameters. While the Schmid-Bulgadaev phase transition persists in the transmon regime, it is driven exclusively by capacitive coupling. The Cooper pair box limit maps to the anisotropic Kondo model with a forbidden ferromagnetic phase.