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arXiv:1301.3494 · Physical Review B

Real-space parallel density matrix renormalization group

Edwin Miles Stoudenmire, Steven R. White

Published Apr 22, 2013• 90 citations
arXivHTMLPDF

Abstract

We demonstrate how to parallelize the density matrix renormalization group (DMRG) algorithm in real space through a straightforward modification of serial DMRG. This makes it possible to apply at least an order of magnitude more computational power to challenging simulations, greatly accelerating investigations of two-dimensional systems and large parameter spaces. We discuss details of the algorithm and present benchmark results including a study of valence-bond-solid order within the square-lattice ${Q}_{2}$ model and N\'eel order within the triangular lattice Heisenberg model. The parallel DMRG algorithm also motivates an alternative canonical form for matrix product states.

DOI
10.1103/physrevb.87.155137

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Abstract: In the last decades, many algorithms have been developed to use high-performance computing (HPC) techniques to accelerate the density matrix renormalization group (DMRG) method, an effective method for solving large active space strong correlation problems. In this article, the previous DMRG parallelization algorithms at different levels of the parallelism are introduced. The heterogeneous computing acceleration methods and the mixed-precision implementation are also presented and discussed. This mini-review concludes with some summary and prospects for future works.