All-atom computations with irreversible Markov chains

Michael F. Faulkner, Liang Qin, Anthony C. Maggs and Werner Krauth

Links: arXiv and DOI.

The event-chain Monte Carlo (ECMC) method is an irreversible Markov process based on the factorized Metropolis filter and the concept of lifted Markov chains. We extended ECMC to all-atom models of multi-particle interactions that include the long-ranged Coulomb potential. For a three-dimensional systems composed of charge-neutral molecules, the algorithmic complexity to advance N particles an O(1) distance is O(N log N). Our particle-particle ECMC method achieved this without the interpolating mesh required for the efficient implementation of other modern Coulomb algorithms. An event-driven, cell-veto-based implementation samples the equilibrium Boltzmann distribution using neither time-step approximations nor spatial cutoffs on the range of the interaction potentials. This opened up many prospects for ECMC in soft condensed-matter and biological physics.