A cluster algorithm for resistively shunted Josephson junctions

TL;DR

This paper introduces a novel cluster algorithm that significantly enhances sampling efficiency for resistively shunted Josephson junctions, enabling detailed analysis of their localization transition and temperature-dependent resistance behavior.

Contribution

The paper develops a new cluster algorithm combining Fourier space updates with symmetry-based cluster moves for Josephson junctions, improving simulation efficiency.

Findings

The algorithm effectively captures the localization transition.

It accurately determines the temperature dependence of zero bias resistance.

The method offers a new tool for studying dissipative quantum systems.

Abstract

We present a cluster algorithm for resistively shunted Josephson junctions and similar physical systems, which dramatically improves sampling efficiency. The algorithm combines local updates in Fourier space with rejection-free cluster updates which exploit the symmetries of the Josephson coupling energy. As an application, we consider the localization transition of a single junction at intermediate Josephson coupling and determine the temperature dependence of the zero bias resistance as a function of dissipation strength.