Cluster Monte Carlo Algorithms for Dissipative Quantum Systems

Dissipation and decoherence in quantum systems have important practical implications, from stabilizing superconductivity in granular materials, to the loss of information stored in qubits. In all the models we study, energy dissipation is introduced by coupling a quantum mechanical degree of freedom to a bath of suitably chosen harmonic oscillators. The degrees of freedom of this bath can be integrated out analytically, which leads to an effective action with long-range interactions in imaginary time. In this article we will review and present a number of recently developed efficient cluster Monte Carlo algorithms for various dissipative quantum systems. These algorithms have been used to study spin chains with dissipation coupling to the site variables and resistively shunted Josephson junctions.1)–7) We will also present relevant theoretical background for these models and mention the open questions which have been addressed in the numerical investigations.