Markov Chain Monte Carlo Method without Detailed Balance

TL;DR

This paper introduces a novel MCMC algorithm that relaxes the detailed balance condition, reducing rejection rates and accelerating convergence, demonstrated by significant improvements in autocorrelation times for the Potts model.

Contribution

The authors develop an MCMC method that satisfies the balance condition without detailed balance, leading to faster convergence and lower rejection rates, applicable to quantum spin models.

Findings

Autocorrelation time for the Potts model is over 6 times shorter.

Rejection rate is minimized and can be zero in relevant cases.

A bounce-free worm algorithm for quantum spin models is formulated.

Abstract

We present a specific algorithm that generally satisfies the balance condition without imposing the detailed balance in the Markov chain Monte Carlo. In our algorithm, the average rejection rate is minimized, and even reduced to zero in many relevant cases. The absence of the detailed balance also introduces a net stochastic flow in a configuration space, which further boosts up the convergence. We demonstrate that the autocorrelation time of the Potts model becomes more than 6 times shorter than that by the conventional Metropolis algorithm. Based on the same concept, a bounce-free worm algorithm for generic quantum spin models is formulated as well.