Cluster Monte Carlo Algorithms for Dissipative Quantum Systems

Abstract

We review efficient Monte Carlo methods for simulating quantum systems which couple to a dissipative environment. A brief introduction of the Caldeira-Leggett model and the Monte Carlo method will be followed by a detailed discussion of cluster algorithms and the treatment of long-range interactions. Dissipative quantum spins and resistively shunted Josephson junctions will be considered.

to be publushed in Proceedings of the Yukawa Symposium 2004

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• First-order transitions in spin chains coupled to quantum baths
• Critical properties of dissipative quantum spin systems in finite dimensions
• Criticality of compact and noncompact quantum dissipative $Z_4$ models in $(1+1)$ dimensions
• Quantum-Classical Transition in Dissipative Double-Well Systems --A Numerical Study by a New Monte Carlo Scheme--