Comment on "Absence versus Presence of Dissipative Quantum Phase Transition in Josephson Junctions''

TL;DR

This paper critiques a recent study on Josephson junctions, arguing that their numerical method is uncontrolled and that their claimed re-entrant superconductivity is not supported by the presented data.

Contribution

It provides a critical analysis of the previous work, challenging the validity of their numerical results and the existence of re-entrant superconductivity.

Findings

NRG implementation is uncontrolled in the referenced study

No evidence for re-entrant superconductivity in the original phase diagram

Questions the validity of the phase features claimed in prior work

Abstract

In a recent Letter [Phys. Rev. Lett. 129, 087001, (2022)], Masuki, Sudo, Oshikawa, and Ashida studied a Josephson junction, with Josephson energy $E_{\rm J}$ and charging energy $E_{\rm C}$, shunted by an ohmic transmission line with conductance $\alpha (2e)^2/h$. Their model includes a realistic high frequency cutoff of order $\alpha E_c$, that is typically smaller than the plasma frequency $W$. The authors present a phase diagram showing surprising features, not anticipated in the established literature [eg. Sch\"on and Zaikin, Phys. Reports 198, 237, (1990)]. For $E_{\rm J}/E_{\rm C}$ above a certain value, they find that the junction remains superconducting for all $\alpha$, while below this value, they find that the insulating phase leads to re-entrant superconductivity at small $\alpha$. In this Comment, we show that their Numerical Renormalization Group (NRG) implementation is uncontrolled, and that there is no evidence for the re-entrant superconductivity in the phase diagram presented in Fig. 1a of PRL 129, 087001.