Many-Configuration Markov-Chain Monte Carlo

TL;DR

This paper introduces a generalized Markov-Chain Monte Carlo method that visits multiple configurations per step, significantly improving efficiency in parallel computing and biased configuration evaluation, demonstrated on spin-glass and Fermi-Hubbard models.

Contribution

It presents a minimal generalization of MCMC allowing multiple configurations per step, enabling faster thermalization and computation in complex models.

Findings

Reduced thermalization time for spin-glass model

Speeded up Fermi-Hubbard calculations by two orders of magnitude

Effective utilization of biased configurations in Monte Carlo sampling

Abstract

We propose a minimal generalization of the celebrated Markov-Chain Monte Carlo algorithm which allows for an arbitrary number of configurations to be visited at every Monte Carlo step. This is advantageous when a parallel computing machine is available, or when many biased configurations can be evaluated at little additional computational cost. As an example of the former case, we report a significant reduction of the thermalization time for the paradigmatic Sherrington-Kirkpatrick spin-glass model. For the latter case, we show that, by leveraging on the exponential number of biased configurations automatically computed by Diagrammatic Monte Carlo, we can speed up computations in the Fermi-Hubbard model by two orders of magnitude.