Lifted directed-worm algorithm

TL;DR

This paper introduces an optimized nonreversible Markov chain algorithm, the lifted directed-worm algorithm, which significantly improves sampling efficiency for the 4D Ising model by maximizing stochastic flow and minimizing backscattering.

Contribution

The paper applies the lifting technique to the directed-worm algorithm, optimizing transition probabilities to enhance performance over existing algorithms.

Findings

Sampling efficiency is 80 times higher than the standard worm algorithm.

Efficiency is 5 times higher than the Wolff cluster algorithm.

Efficiency is 1.7 times higher than the previous lifted 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.