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

Abstract

In a recent Letter [Phys. Rev. Lett. 129, 087001, (2022)], Masuki, Sudo, Oshikawa, and Ashida studied a Josephson junction, with Josephson energy $E_{\mathrm{J}}$ and charging energy $E_{\mathrm{C}}$, 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. Schön and Zaikin, Phys. Reports 198, 237, (1990)]. For $E_{\mathrm{J}}/E_{\mathrm{C}}$ 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.

3 pages. Text of the version accepted for publication, plus an appendix with additional information

References in corpus (2)

• The numerical renormalization group method for quantum impurity systems
• Absence versus Presence of Dissipative Quantum Phase Transition in Josephson Junctions

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