Generic placeholder image

Current Chinese Science

Author(s): Yingqi Tian* and Haibo Ma

DOI: 10.2174/2210298103666221125162959

DownloadDownload PDF Flyer Cite As
High-Performance Computing for Density Matrix Renormalization Group

Page: [178 - 186] Pages: 9

  • * (Excluding Mailing and Handling)

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.

Graphical Abstract

[1]
White, S.R. Density matrix formulation for quantum renormalization groups. Phys. Rev. Lett., 1992, 69(19), 2863-2866.
[http://dx.doi.org/10.1103/PhysRevLett.69.2863] [PMID: 10046608]
[2]
White, S.R. Density-matrix algorithms for quantum renormalization groups. Phys. Rev. B Condens. Matter, 1993, 48(14), 10345-10356.
[http://dx.doi.org/10.1103/PhysRevB.48.10345] [PMID: 10007313]
[3]
Shuai, Z.; Brédas, J.L.; Pati, S.K.; Ramasesha, S. Quantum-confinement effects on the ordering of the lowest-lying excited states in conjugated chains. Phys. Rev. B Condens. Matter, 1997, 56(15), 9298-9301.
[http://dx.doi.org/10.1103/PhysRevB.56.9298]
[4]
White, S.R.; Martin, R.L. Ab initio quantum chemistry using the density matrix renormalization group. J. Chem. Phys., 1999, 110(9), 4127-4130.
[http://dx.doi.org/10.1063/1.478295]
[5]
Chan, G.K.L.; Head-Gordon, M. Highly correlated calculations with a polynomial cost algorithm: A study of the density matrix renormalization group. J. Chem. Phys., 2002, 116(11), 4462-4476.
[http://dx.doi.org/10.1063/1.1449459]
[6]
Moritz, G.; Hess, B.A.; Reiher, M. Convergence behavior of the density-matrix renormalization group algorithm for optimized orbital orderings. J. Chem. Phys., 2005, 122(2), 024107.
[http://dx.doi.org/10.1063/1.1824891] [PMID: 15638572]
[7]
Zhai, H.; Chan, G.K.L. Low communication high performance ab initio density matrix renormalization group algorithms. J. Chem. Phys., 2021, 154(22), 224116.
[http://dx.doi.org/10.1063/5.0050902] [PMID: 34241198]
[8]
Chandra, R.; Dagum, L.; Kohr, D.; Menon, R.; Maydan, D.; McDonald, J. Parallel programming. In: Open MP; , 2001; 2001, .
[9]
Forum, M.P. MPI: A Message-Passing Interface Standard; University of Tennessee: USA, 1994.
[10]
NVIDIA. CUDA toolkit documentation v12.0. 2022. Available from: http://docs.nvidia.com/cuda/
[11]
AMD. New AMD ROCm™ Information Portal - ROCm v4.5 and Above., 2022. Available from: https://rocmdocs.amd.com/en/latest/
[12]
The Khronos Group Inc. OpenCL Overview., 2022. Available from: https://www.khronos.org/api/opencl
[13]
Chan, G.K.L.; Sharma, S. The density matrix renormalization group in quantum chemistry. Annu. Rev. Phys. Chem., 2011, 62(1), 465-481.
[http://dx.doi.org/10.1146/annurev-physchem-032210-103338] [PMID: 21219144]
[14]
Kurashige, Y. Multireference electron correlation methods with density matrix renormalisation group reference functions. Mol. Phys., 2014, 112(11), 1485-1494.
[http://dx.doi.org/10.1080/00268976.2013.843730]
[15]
Wouters, S.; Van Neck, D. The density matrix renormalization group for ab initio quantum chemistry. Eur. Phys. J. D, 2014, 68(9), 272.
[http://dx.doi.org/10.1140/epjd/e2014-50500-1]
[16]
Baiardi, A.; Reiher, M. The density matrix renormalization group in chemistry and molecular physics: Recent developments and new chal-lenges. J. Chem. Phys., 2020, 152(4), 040903.
[http://dx.doi.org/10.1063/1.5129672] [PMID: 32007028]
[17]
Freitag, L.; Reiher, M. The Density Matrix Renormalization Group for Strong Correlation in Ground and Excited States; Gonzalez, L. In: Quantum Chemistry and Dynamics of Excited States; Lindh, R., Ed.; John Wiley & Sons, Ltd: Hoboken, 2020; pp. 205-245.
[18]
Cheng, Y.; Xie, Z.; Ma, H. Post-Density Matrix Renormalization Group Methods for Describing Dynamic Electron Correlation with Large Active Spaces. J. Phys. Chem. Lett., 2022, 13(3), 904-915.
[http://dx.doi.org/10.1021/acs.jpclett.1c04078] [PMID: 35049302]
[19]
Hager, G.; Jeckelmann, E.; Fehske, H.; Wellein, G. Parallelization strategies for density matrix renormalization group algorithms on shared-memory systems. J. Comput. Phys., 2004, 194(2), 795-808.
[http://dx.doi.org/10.1016/j.jcp.2003.09.018]
[20]
Kurashige, Y.; Yanai, T. High-performance ab initio density matrix renormalization group method: Applicability to large-scale multireference problems for metal compounds. J. Chem. Phys., 2009, 130(23), 234114.
[http://dx.doi.org/10.1063/1.3152576] [PMID: 19548718]
[21]
Levy, R.; Solomonik, E.; Clark, B.K. distributed-memory dmrg via sparse and dense parallel tensor contractions Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis, Atlanta, Georgia2020.
[http://dx.doi.org/10.1109/SC41405.2020.00028]
[22]
Chan, G.K.L. An algorithm for large scale density matrix renormalization group calculations. J. Chem. Phys., 2004, 120(7), 3172-3178.
[http://dx.doi.org/10.1063/1.1638734] [PMID: 15268469]
[23]
Chan, G.K.L.; Keselman, A.; Nakatani, N.; Li, Z.; White, S.R. Matrix product operators, matrix product states, and ab initio density matrix renormalization group algorithms. J. Chem. Phys., 2016, 145(1), 014102.
[http://dx.doi.org/10.1063/1.4955108] [PMID: 27394094]
[24]
Stoudenmire, E.M.; White, S.R. Real-space parallel density matrix renormalization group. Phys. Rev. B Condens. Matter Mater. Phys., 2013, 87(15), 155137.
[http://dx.doi.org/10.1103/PhysRevB.87.155137]
[25]
Secular, P.; Gourianov, N.; Lubasch, M.; Dolgov, S.; Clark, S.R.; Jaksch, D. Parallel time-dependent variational principle algorithm for matrix product states. Phys. Rev. B, 2020, 101(23), 235123.
[http://dx.doi.org/10.1103/PhysRevB.101.235123]
[26]
Chen, F.Z.; Cheng, C.; Luo, H-G. Real-space parallel density matrix renormalization group with adaptive boundaries. Chin. Phys. B, 2021, 30(8), 080202.
[http://dx.doi.org/10.1088/1674-1056/abeb08]
[27]
Brabec, J.; Brandejs, J.; Kowalski, K.; Xantheas, S.; Legeza, Ö.; Veis, L. Massively parallel quantum chemical density matrix renormalization group method. J. Comput. Chem., 2021, 42(8), 534-544.
[http://dx.doi.org/10.1002/jcc.26476] [PMID: 33377527]
[28]
Nemes, C.; Barcza, G.; Nagy, Z.; Legeza, Ö.; Szolgay, P. The density matrix renormalization group algorithm on kilo-processor architectures: Implementation and trade-offs. Comput. Phys. Commun., 2014, 185(6), 1570-1581.
[http://dx.doi.org/10.1016/j.cpc.2014.02.021]
[29]
Chen, F.Z.; Cheng, C.; Luo, H.G. Hybrid parallel optimization of density matrix renormalization group method. Wuli Xuebao, 2019, 68(12), 120202.
[http://dx.doi.org/10.7498/aps.68.20190586]
[30]
Chen, F.Z.; Cheng, C.; Luo, H-G. Improved hybrid parallel strategy for density matrix renormalization group method. Chin. Phys. B, 2020, 29(7), 070202.
[http://dx.doi.org/10.1088/1674-1056/ab8a42]
[31]
Li, W.; Ren, J.; Shuai, Z. Numerical assessment for accuracy and GPU acceleration of TD-DMRG time evolution schemes. J. Chem. Phys., 2020, 152(2), 024127.
[http://dx.doi.org/10.1063/1.5135363] [PMID: 31941314]
[32]
Ganahl, M.; Beall, J.; Hauru, M.; Lewis, A.G.M.; Yoo, J.H.; Zou, Y.; Vidal, G. density matrix renormalization group with tensor processing units. arXiv, 2022.
[33]
Tian, Y.; Xie, Z.; Luo, Z; Ma, H. Mixed-Precision Implementation of the Density Matrix Renormalization Group. J. Chem. Theory Comput., 2022.
[http://dx.doi.org/10.1021/acs.jctc.2c00632]