Algorithm for branching and population control in correlated sampling

Correlated sampling can have wide-ranging applications in quantum Monte Carlo (QMC) calculations, especially for computing energy differences or gradients in systems in proximity to each other. For example, it has been applied to chemical systems with the phaseless auxiliary field quantum Monte Carlo (AFQMC) method[1] to obtain accurate bond dissociation energies, ionization potentials, and electron affinities[2]. When branching random walks are involved, which is often the case in QMC applications, population control is typically not applied with correlated sampling, because of technical challenges. This hinders the stability and efficiency of correlated sampling, especially in larger system sizes or physically more challenging systems, when branching is more pronounced. In this work, we study schemes for allowing birth/death in correlated sampling, and propose two algorithms for population control. The first is a static method which creates a reference run and allows other correlated calculations to be added a posterior, while the second optimizes the population control for a set of correlated, concurrent runs dynamically. The two approaches are tested in different applications, including both the Hubbard model and real materials.

[1] Shiwei Zhang. Auxiliary-Field Quantum Monte Carlo at Zero- and Finite- Temperature, volume 9. Verlag des Forschungszentrum Jülich, Jülich, Germany, 2019.

[2] James Shee, Shiwei Zhang, David R. Reichman, and Richard A. Friesner. Journal of chemical theory and computation, 13 6:2667–2680, 2017.