Lifted directed-worm algorithm

Abstract

Nonreversible Markov chains can outperform reversible chains in the Markov chain Monte Carlo method. Lifting is a versatile approach to introducing net stochastic flow in state space and constructing a nonreversible Markov chain. We present here an application of the lifting technique to the directed-worm algorithm. The transition probability of the worm update is optimized using the geometric allocation approach; the worm backscattering probability is minimized, and the stochastic flow breaking the detailed balance is maximized. We demonstrate the performance improvement over the previous worm and cluster algorithms for the four-dimensional hypercubic lattice Ising model. The sampling efficiency of the present algorithm is approximately 80, 5, and 1.7 times as high as those of the standard worm algorithm, the Wolff cluster algorithm, and the previous lifted worm algorithm, respectively. We estimate the dynamic critical exponent of the hypercubic lattice Ising model to be $z\approx 0$ in the worm and the Wolff cluster updates. The lifted version of the directed-worm algorithm can be applied to a variety of quantum systems as well as classical systems.

10 pages, 3 figures

References in corpus (9)

• Worm Algorithm and Diagrammatic Monte Carlo: A New Approach to Continuous-Space Path Integral Monte Carlo Simulations
• Quantum Monte Carlo simulations of confined bosonic atoms in optical lattices
• Markov Chain Monte Carlo Method without Detailed Balance
• Accelerating diffusions
• Order-N Cluster Monte Carlo Method for Spin Systems with Long-range Interactions
• Critical behaviour of the Ising model on the 4-dimensional lattice
• Worm Improved Estimators in Continuous-time Quantum Monte Carlo
• Worm algorithms for the 3-state Potts model with magnetic field and chemical potential
• Worm Monte Carlo study of the honeycomb-lattice loop model

Cited by in corpus (1)

• Reducing rejection exponentially improves Markov chain Monte Carlo sampling