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.

arXiv comment3 pages. Text of the version accepted for publication, plus an appendix with additional information

References in corpus (3)

• The numerical renormalization group method for quantum impurity systems
• Absence versus Presence of Dissipative Quantum Phase Transition in Josephson Junctions
• Numerical Renormalization Group at marginal spectral density: application to quantum tunneling in Luttinger liquids

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