Quantum effects on the BKT phase transition of two-dimensional Josephson arrays

TL;DR

This paper investigates how quantum effects influence the Berezinskii-Kosterlitz-Thouless phase transition in two-dimensional Josephson arrays using a semiclassical approximation and models dissipation, providing a practical method for calculating critical temperatures.

Contribution

It introduces a semiclassical approach to accurately evaluate quantum and dissipative effects on the BKT transition in Josephson arrays, improving upon previous quantum Monte Carlo results.

Findings

Quantum effects significantly alter the critical temperature.

The semiclassical method provides an easy way to compute phase transition points.

Experimental data suggest the standard model may not fully capture real system behavior.

Abstract

The phase diagram of two dimensional Josephson arrays is studied by means of the mapping to the quantum XY model. The quantum effects onto the thermodynamics of the system can be evaluated with quantitative accuracy by a semiclassical method, the {\em pure-quantum self-consistent harmonic approximation}, and those of dissipation can be included in the same framework by the Caldeira-Leggett model. Within this scheme, the critical temperature of the superconductor-to-insulator transition, which is a Berezinskii-Kosterlitz-Thouless one, can be calculated in an extremely easy way as a function of the quantum coupling and of the dissipation mechanism. Previous quantum Monte Carlo results for the same model appear to be rather inaccurate, while the comparison with experimental data leads to conclude that the commonly assumed model is not suitable to describe in detail the real system.