Engineering Local optimality in Quantum Monte Carlo algorithms

Abstract

Quantum Monte Carlo algorithms based on a world-line representation such as the worm algorithm and the directed loop algorithm are among the most powerful numerical techniques for the simulation of non-frustrated spin models and of bosonic models. Both algorithms work in the grand-canonical ensemble and have a non-zero winding number. However, they retain a lot of intrinsic degrees of freedom which can be used to optimize the algorithm. We let us guide by the rigorous statements on the globally optimal form of Markov chain Monte Carlo simulations in order to devise a locally optimal formulation of the worm algorithm while incorporating ideas from the directed loop algorithm. We provide numerical examples for the soft-core Bose-Hubbard model and various spin-S models.

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References in corpus (7)

• Generalized Directed Loop Method for Quantum Monte Carlo Simulations
• Recent Developments of World-Line Monte Carlo Methods
• Directed Loop Updates for Quantum Lattice Models
• Loop updates for quantum Monte Carlo simulations in the canonical ensemble
• Optimal Monte Carlo Updating
• Quantum Monte Carlo simulation in the canonical ensemble at finite temperature
• Bosons in optical lattices - from the Mott transition to the Tonks-Girardeau gas

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