On the nature of the Schmid transition in a resistively shunted Josephson junction

Abstract

We study the phase diagram of a resistively shunted Josephson junction (RSJJ) in the framework of the boundary sine-Gordon model. Using the non-perturbative functional renormalization group (FRG) we find that the transition is not controlled by a single fixed point but by a line of fixed points, and compute the continuously varying critical exponent $\nu$. We argue that the conductance also varies continuously along the transition line. In contrast to the traditional phase diagram of the RSJJ -- an insulating ground state when the shunt resistance $R$ is larger than $R_q=h/(2e{)}^2$ and a superconducting one when $R<R_q$ -- the FRG predicts the transition line in the plane $(\alpha ,E_J/E_C)$ to bend in the region $\alpha =R_q/R<1$ but we cannot discard the possibility of a vertical line at $\alpha =1$ ($E_J$ and $E_C$ denote the Josephson and charging energies of the junction, respectively). Our results regarding the phase diagram and the nature of the transition are compared with Monte Carlo simulations and numerical renormalization group results.

15 pages, 15 figures ; v2 closer to published version

References in corpus (13)

• Exact evolution equation for the effective potential
• The nonperturbative functional renormalization group and its applications
• Impurity and correlation effects on transport in one-dimensional quantum wires
• Reexamination of the nonperturbative renormalization-group approach to the Kosterlitz-Thouless transition
• Higgs amplitude mode in the vicinity of a $(2+1)$-dimensional quantum critical point: a nonperturbative renormalization-group approach
• A cluster algorithm for resistively shunted Josephson junctions
• Absence versus Presence of Dissipative Quantum Phase Transition in Josephson Junctions
• Fermionic renormalization group methods for transport through inhomogeneous Luttinger liquids
• Appearance of ferroelectricity in thin films of incipient ferroelectric
• Nonperturbative functional renormalization-group approach to transport in the vicinity of a $(2+1)$-dimensional O($N$)-symmetric quantum critical point
• Nonperturbative fluctuations and metastability in a simple model: from observables to microscopic theory and back
• Physical properties of the massive Schwinger model from the nonperturbative functional renormalization group
• Functional Renormalization Group Approach to Circuit Quantum Electrodynamics

Cited by in corpus (9)

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• Observation of the Schmid-Bulgadaev dissipative quantum phase transition
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• Resilience of the quantum critical line in the Schmid transition
• Universal Crossover in the Three-Channel Charge Kondo Model at High Transparency
• Interaction-induced dissipative quantum phase transition in a head-to-tail atomic Josephson junction
• Revisiting dissipation-driven phase transition in a Josephson junction
• Absence of a dissipative quantum phase transition in Josephson junctions: Theory