The inherent complexity of system-bath interactions often requires making critical approximations, which we here show to have a radical influence on the renormalization group flow and the resulting phase diagram. Specifically, for the Caldeira-Leggett model Schmid and Bulgadaev (SB) predicted a phase transition, whose experimental verification in resistive superconducting circuits is currently hotly debated. For normal metal and Josephson junction array resistors, we show that the mapping to Caldeira-Leggett is only exact when applying approximations which decompactify the superconducting phase. We show that there exist treatments that retain phase compactness, which immediately lead to a phase diagram depending on four instead of two parameters. While we still find an SB-like transition in the transmon regime, the critical parameter is controlled exclusively by the capacitive coupling. In contrast, the Cooper pair box maps to the anisotropic Kondo model, where a pseudoferromagnetic phase is not allowed for regular electrostatic interactions.

中文翻译：

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Caldeira-Leggett 模型在描述超导电路中相变方面的局限性


系统-浴相互作用的固有复杂性通常需要进行临界近似，我们在这里表明，这对重整化群流和所得相图有根本性的影响。具体来说，对于 Caldeira-Leggett 模型，Schmid 和 Bulgadaev （SB） 预测了相变，其在电阻超导电路中的实验验证目前正处于激烈争论中。对于普通金属和 Josephson 结阵列电阻器，我们表明，只有在应用使超导相解压缩的近似值时，到 Caldeira-Leggett 的映射才是精确的。我们表明，存在保持相紧凑性的处理，这立即导致相图取决于四个而不是两个参数。虽然我们仍然在 transmon 机制中发现类似 SB 的转变，但关键参数完全由电容耦合控制。相比之下，Cooper 对框映射到各向异性 Kondo 模型，其中不允许使用伪铁磁相进行常规的静电相互作用。