Schmid 转变中量子临界线的鲁棒性
Resilience of the quantum critical line in the Schmid transition
AI总结：
本文通过场论重正化群、费米子模型和绝热方法，严格证明 Schmid 转变中量子临界线位置不依赖于约瑟夫森与充电能量之比，并保持鲁棒性。
摘要：
Schmid 预言，当分流电阻 $R$ 超过电阻量子 $h/(4 e^2)$ 时，耦合到电阻环境的单个约瑟夫森结会发生量子相变，转变为绝缘相。最近的测量和理论研究引发了关于该转变位置是否依赖于约瑟夫森能量与充电能量之比的争论。我们结合多种创新的解析和数值技术（这些技术此前从未明确应用于该问题），决定性地证明超导行为与绝缘行为之间的转变线确实与该能量比无关。首先，我们应用场论重正化群方法，发现 $\eta$ 函数在临界线上直至约瑟夫森能量的三阶都为零。然后，我们确定了一个简单的费米子模型，该模型精确捕捉了临界线上的低能物理，无论能量比如何。通过将预期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，验证了这一共形不变的费米子模型，即使在中等系统尺寸下也表现出极好的一致性。重要的是，这一识别提供了严格的非微扰证明，即转变线保持在 $R=h/(4 e^2)$，与约瑟夫森能量和充电能量的所有比值无关。该线对电阻环境的等离子体频率等其他紫外截断也具有鲁棒性。最后，我们实现了一种绝热方法来验证大约瑟夫森能量下的对偶性。
英文摘要：
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 $β$ 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.
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