Parallelized Quantum Monte Carlo Algorithm with Nonlocal Worm Updates

TL;DR

This paper introduces a parallel quantum Monte Carlo algorithm based on the worm method, enabling efficient simulation of large lattice systems of bosons and spins on distributed-memory computers.

Contribution

It presents a novel parallelization approach for quantum Monte Carlo algorithms using domain decomposition and nonlocal worm updates, suitable for large-scale simulations.

Findings

Achieved efficient parallelization on 3200 cores for large lattice systems.

Demonstrated scalability with a 10240x10240x16 lattice size.

Validated the algorithm with the Bose-Hubbard model benchmark.

Abstract

Based on the worm algorithm in the path-integral representation, we propose a general quantum Monte Carlo algorithm suitable for parallelizing on a distributed-memory computer by domain decomposition. Of particular importance is its application to large lattice systems of bosons and spins. A large number of worms are introduced and its population is controlled by a fictitious transverse field. For a benchmark, we study the size-dependence of the Bose-condensation order parameter of the hardcore Bose-Hubbard model with $L\times L\times \beta t = 10240\times 10240\times 16$, using 3200 computing cores, which shows good parallelization efficiency.