标题： 施密德转变中量子临界线的韧性 显示英文标题

标题： Resilience of the quantum critical line in the Schmid transition

摘要： 施密德预测，一个耦合到电阻环境的单个约瑟夫森结当旁路电阻 $R$ 超过量子电阻 $h/(4 e^ 2)$ 时，会经历一个量子相变进入绝缘态。 最近的测量和理论研究引发了关于这一转变位置是否依赖于约瑟夫森能和充电能之比的争论。 我们采用了一种从未明确应用于该问题的多种创新性解析和数值技术组合，明确证明了超导与绝缘行为之间的转变线确实独立于这个能量比。 首先，我们应用场论重正化群方法，并发现约瑟夫森能的三次项内临界线上 $\beta$ 函数消失。 然后，我们识别出一个简单的费米子模型，无论能量比如何，它都能精确捕捉临界线上的低能物理。 通过将预期的谱与电阻分流约瑟夫森结的精确对角化计算结果进行比较验证了这个共形不变的费米子模型，即使对于中等大小的系统也显示出极好的一致性。 重要的是，这种识别提供了一个严格的非微扰证明，即转变线在所有约瑟夫森能与充电能之比下都保持在 $R=h/(4 e^ 2)$。 这条线还对其他紫外截断具有弹性，例如电阻环境的等离子体频率。 最后，我们采用绝热方法验证了大约瑟夫森能下的对偶性。 显示英文摘要

摘要： Schmid predicted that a single Josephson junction coupled to a resistive environment undergoes a quantum phase transition to an insulating phase when the shunt resistance $R$ exceeds the resistance quantum $h/(4 e^ 2)$. Recent measurements and theoretical studies have sparked a debate on whether the location of this transition depends on the ratio between the Josephson and the charging energies. We employ a combination of multiple innovative analytical and numerical techniques, never before explicitly applied to this problem, to decisively demonstrate that the transition line between superconducting and insulating behavior is indeed independent of this energy ratio. First, we apply field-theory renormalization group methods and find that the $\beta$ function vanishes along the critical line up to the third order in the Josephson energy. We then identify a simple fermionic model that precisely captures the low-energy physics on the critical line, regardless of the energy ratio. This conformally invariant fermionic model is verified by comparing the expected spectrum with exact diagonalization calculations of the resistively shunted Josephson junction, showing excellent agreement even for moderate system sizes. Importantly, this identification provides a rigorous non-perturbative proof that the transition line is maintained at $R=h/(4 e^ 2)$ for all ratios of Josephson to charging energies. The line is further resilient to other ultraviolet cutoffs such as the plasma frequency of the resistive environment. Finally, we implement an adiabatic approach to validate the duality at large Josephson energy.