Monte Carlo Method Controlling Probability Flow―Detailed Balance Breaking and Lifting

Abstract

Since being invented in the 1950s, the Markov chain Monte Carlo method has evolved within the paradigm of detailed balance, namely, reversibility. However, detailed balance is not necessary for numerical integration, and net probability flow can significantly accelerate distribution convergence. Efficient non-reversible Monte Carlo algorithms controlling probability flow, such as the lifting technique, have been recently developed for solving many-body problems. In this article, we explain the idea of lifting and review lifted Monte Carlo algorithms, including the event-chain Monte Carlo method and the directed worm algorithm.