Algorithm for branching and population control in correlated sampling

TL;DR

This paper introduces a novel algorithm for population control in correlated sampling involving branching random walks, enhancing stability and efficiency in quantum Monte Carlo simulations.

Contribution

It proposes new schemes for birth/death processes in correlated sampling, including static and dynamic variants, applicable to quantum physics and electronic structure calculations.

Findings

Improved stability in Monte Carlo calculations with branching processes

Effective population control in quantum system simulations

Versatile algorithms tested on Hubbard model and real materials

Abstract

Correlated sampling has wide-ranging applications in Monte Carlo calculations. When branching random walks are involved, as commonly found in many algorithms in quantum physics and electronic structure, population control is typically not applied with correlated sampling due to technical difficulties. This hinders the stability and efficiency of correlated sampling. In this work, we study schemes for allowing birth/death in correlated sampling and propose an algorithm for population control. The algorithm can be realized in several variants depending on the application. One variant is a static method that creates a reference run and allows other correlated calculations to be added a posteriori. Another optimizes the population control for a set of correlated, concurrent runs dynamically. These approaches are tested in different applications in quantum systems, including both the Hubbard model and electronic structure calculations in real materials.