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Bulletin of the American Physical Society

Parallelized Multi-Worm Algorithm for Large Scale Quantum Monte-Carlo simulations

Takafumi J. Suzuki, Akiko Masaki-Kato, Kenji Harada, Synge Todo, Naoki Kawashima

Published Mar 3, 2014• 0 citations
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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 hard-core Bose-Hubbard model with $L\ifmmode\times\else\texttimes\fi{}L\ifmmode\times\else\texttimes\fi{}\ensuremath{\beta}t=10240\ifmmode\times\else\texttimes\fi{}10240\ifmmode\times\else\texttimes\fi{}16$, using 3200 computing cores, which shows good parallelization efficiency.
The generic Mott transition in one-dimensional quantum systems can be described by the sine-Gordon model with a tilt via bosonization. Because the configuration space of the sine-Gordon model separates into distinct topological sectors, standard local Monte Carlo schemes are limited to very small system sizes. To overcome this limitation, we introduce the smooth worm (SmoWo) Monte Carlo algorithm which enlarges the configuration space to allow smooth transitions between topological sectors. The method combines worm updates with event-chain Monte Carlo moves. We explicitly prove its validity and quantify its performance. Thanks to the substantial acceleration achieved by the SmoWo algorithm, we are able to simulate large system sizes, providing a precise picture of the different phases and critical behaviour of the sine-Gordon model.