Optimal Monte Carlo Updating

Abstract

Based on Peskun's theorem it is shown that optimal transition matrices in Markov chain Monte Carlo should have zero diagonal elements except for the diagonal element corresponding to the largest weight. We will compare the statistical efficiency of this sampler to existing algorithms, such as heat-bath updating and the Metropolis algorithm. We provide numerical results for the Potts model as an application in classical physics. As an application in quantum physics we consider the spin 3/2 XY model and the Bose-Hubbard model which have been simulated by the directed loop algorithm in the stochastic series expansion framework.

6 pages, 5 figures, replaced with published version

References in corpus (13)

• An efficient, multiple range random walk algorithm to calculate the density of states
• Quantum Monte Carlo with Directed Loops
• Stochastic series expansion method with operator-loop update
• Cluster Algorithm for Vertex Models
• The Loop Algorithm
• Strict Detailed Balance is Unnecessary in Monte Carlo Simulation
• Recent Developments of World-Line Monte Carlo Methods
• Accessing the dynamics of large many-particle systems using Stochastic Series Expansion
• Exact Quantum Monte Carlo Process for the Statistics of Discrete Systems
• A quantum Monte-Carlo method for fermions, free of discretization errors
• Directed Loop Updates for Quantum Lattice Models
• Bosons Confined in Optical Lattices: the Numerical Renormalization Group revisited
• Universal SSE algorithm for Heisenberg model and Bose Hubbard model with interaction

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