Improved hybrid parallel strategy for density matrix renormalization group method

doi:10.1088/1674-1056/ab8a42

中国物理B ›› 2020, Vol. 29 ›› Issue (7): 70202-070202.doi: 10.1088/1674-1056/ab8a42

Improved hybrid parallel strategy for density matrix renormalization group method

Fu-Zhou Chen(陈富州), Chen Cheng(程晨), Hong-Gang Luo(罗洪刚)

1 School of Physical Science and Technology, Lanzhou University, Lanzhou 730000, China;
2 Beijing Computational Science Research Center, Beijing 100084, China

收稿日期:2020-01-21 修回日期:2020-04-07 出版日期:2020-07-05 发布日期:2020-07-05
通讯作者: Hong-Gang Luo E-mail:luohg@lzu.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11674139, 11834005, and 11904145) and the Program for Changjiang Scholars and Innovative Research Team in University, China (Grant No. IRT-16R35).

Improved hybrid parallel strategy for density matrix renormalization group method

Fu-Zhou Chen(陈富州)¹, Chen Cheng(程晨)^1,2, Hong-Gang Luo(罗洪刚)^1,2

1 School of Physical Science and Technology, Lanzhou University, Lanzhou 730000, China;
2 Beijing Computational Science Research Center, Beijing 100084, China

Received:2020-01-21 Revised:2020-04-07 Online:2020-07-05 Published:2020-07-05
Contact: Hong-Gang Luo E-mail:luohg@lzu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11674139, 11834005, and 11904145) and the Program for Changjiang Scholars and Innovative Research Team in University, China (Grant No. IRT-16R35).

摘要/Abstract

摘要： We propose a new heterogeneous parallel strategy for the density matrix renormalization group (DMRG) method in the hybrid architecture with both central processing unit (CPU) and graphics processing unit (GPU). Focusing on the two most time-consuming sections in the finite DMRG sweeps, i.e., the diagonalization of superblock and the truncation of subblock, we optimize our previous hybrid algorithm to achieve better performance. For the former, we adopt OpenMP application programming interface on CPU and use our own subroutines with higher bandwidth on GPU. For the later, we use GPU to accelerate matrix and vector operations involving the reduced density matrix. Applying the parallel scheme to the Hubbard model with next-nearest hopping on the 4-leg ladder, we compute the ground state of the system and obtain the charge stripe pattern which is usually observed in high temperature superconductors. Based on simulations with different numbers of DMRG kept states, we show significant performance improvement and computational time reduction with the optimized parallel algorithm. Our hybrid parallel strategy with superiority in solving the ground state of quasi-two dimensional lattices is also expected to be useful for other DMRG applications with large numbers of kept states, e.g., the time dependent DMRG algorithms.

关键词: density matrix renormalization group, strongly correlated model, hybrid parallelization

Abstract: We propose a new heterogeneous parallel strategy for the density matrix renormalization group (DMRG) method in the hybrid architecture with both central processing unit (CPU) and graphics processing unit (GPU). Focusing on the two most time-consuming sections in the finite DMRG sweeps, i.e., the diagonalization of superblock and the truncation of subblock, we optimize our previous hybrid algorithm to achieve better performance. For the former, we adopt OpenMP application programming interface on CPU and use our own subroutines with higher bandwidth on GPU. For the later, we use GPU to accelerate matrix and vector operations involving the reduced density matrix. Applying the parallel scheme to the Hubbard model with next-nearest hopping on the 4-leg ladder, we compute the ground state of the system and obtain the charge stripe pattern which is usually observed in high temperature superconductors. Based on simulations with different numbers of DMRG kept states, we show significant performance improvement and computational time reduction with the optimized parallel algorithm. Our hybrid parallel strategy with superiority in solving the ground state of quasi-two dimensional lattices is also expected to be useful for other DMRG applications with large numbers of kept states, e.g., the time dependent DMRG algorithms.

Key words: density matrix renormalization group, strongly correlated model, hybrid parallelization

中图分类号: (Computational techniques; simulations)

02.70.-c

71.10.Fd (Lattice fermion models (Hubbard model, etc.)) 71.27.+a (Strongly correlated electron systems; heavy fermions) 05.10.Cc (Renormalization group methods)

陈富州, 程晨, 罗洪刚. Improved hybrid parallel strategy for density matrix renormalization group method[J]. 中国物理B, 2020, 29(7): 70202-070202.

Fu-Zhou Chen(陈富州), Chen Cheng(程晨), Hong-Gang Luo(罗洪刚). Improved hybrid parallel strategy for density matrix renormalization group method[J]. Chin. Phys. B, 2020, 29(7): 70202-070202.

参考文献 43

[1]	White S R 1992 Phys. Rev. Lett. 69 2863 doi: 10.1103/PhysRevLett.69.2863
[2]	White S R 1993 Phys. Rev. B 48 10345 doi: 10.1103/PhysRevB.48.10345
[3]	Schollwöck U 2005 Rev. Mod. Phys. 77 259 doi: 10.1103/RevModPhys.77.259
[4]	Xiang T 1996 Phys. Rev. B 53 R10445
[5]	Ehlers G, White S R and Noack R M 2017 Phys. Rev. B 95 125125 doi: 10.1103/PhysRevB.95.125125
[6]	White S R and Martin R L 1999 J. Chem. Phys. 110 4127 doi: 10.1063/1.478295
[7]	Luo H G, Qin M P and Xiang T 2010 Phys. Rev. B 81 235129 doi: 10.1103/PhysRevB.81.235129
[8]	Yang J, Hu W, Usvyat D, Matthews D, Schütz M and Chan G K L 2014 Science 345 640 doi: 10.1126/science.1254419
[9]	Cazalilla M A and Marston J B 2002 Phys. Rev. Lett. 88 256403 doi: 10.1103/PhysRevLett.88.256403
[10]	Luo H G, Xiang T and Wang X Q 2003 Phys. Rev. Lett. 91 049701 doi: 10.1103/PhysRevLett.91.049701
[11]	White S R and Feiguin A E 2004 Phys. Rev. Lett. 93 076401 doi: 10.1103/PhysRevLett.93.076401
[12]	Verstraete F, García-Ripoll J J and Cirac J I 2004 Phys. Rev. Lett. 93 207204 doi: 10.1103/PhysRevLett.93.207204
[13]	Feiguin A E and White S R 2005 Phys. Rev. B 72 220401 doi: 10.1103/PhysRevB.72.220401
[14]	Stoudenmire E M and White S R 2010 New J. Phys. 12 055026 doi: 10.1088/1367-2630/12/5/055026
[15]	White S R 2009 Phys. Rev. Lett. 102 190601 doi: 10.1103/PhysRevLett.102.190601
[16]	Dagotto E 1994 Rev. Mod. Phys. 66 763 doi: 10.1103/RevModPhys.66.763
[17]	Keimer B, Kivelson S A, Norman M R, Uchida S and Zaanen J 2015 Nature 518 179 doi: 10.1038/nature14165
[18]	Fradkin E, Kivelson S A and Tranquada J M 2015 Rev. Mod. Phys. 87 457 doi: 10.1103/RevModPhys.87.457
[19]	Zheng B X, Chung C M, Corboz P, Ehlers G, Qin M P, Noack R M, Shi H, White S R, Zhang S and Chan G K L 2017 Science 358 1155 doi: 10.1126/science.aam7127
[20]	Huang E W, Mendl C B, Liu S, Johnston S, Jiang H C, Moritz B and Devereaux T P 2017 Science 358 1161 doi: 10.1126/science.aak9546
[21]	Cheng C, Mondaini R and Rigol M 2018 Phys. Rev. B 98 121112 doi: 10.1103/PhysRevB.98.121112
[22]	Huang E W, Mendl C B, Jiang H C, Moritz B and Devereaux T P 2018 npj Quantum Materials 3 22 doi: 10.1038/s41535-018-0097-0
[23]	Yan S, Huse D A and White S R 2011 Science 332 1173 doi: 10.1126/science.1201080
[24]	Savary L and Balents L 2016 Reports on Progress in Physics 80 016502
[25]	Wang L and Sandvik A W 2018 Phys. Rev. Lett. 121 107202 doi: 10.1103/PhysRevLett.121.107202
[26]	Alvarez G 2012 Comput. Phys. Commun. 183 2226 doi: 10.1016/j.cpc.2012.04.025
[27]	Tzeng Y C 2012 Phys. Rev. B 86 024403 doi: 10.1103/PhysRevB.86.024403
[28]	Legeza O, Röder J and Hess B A 2003 Phys. Rev. B 67 125114 doi: 10.1103/PhysRevB.67.125114
[29]	Legeza O and Sólyom J 2003 Phys. Rev. B 68 195116 doi: 10.1103/PhysRevB.68.195116
[30]	Hubig C, McCulloch I P, Schollwöock U and Wolf F A 2015 Phys. Rev. B 91 155115 doi: 10.1103/PhysRevB.91.155115
[31]	White S R 2005 Phys. Rev. B 72 180403 doi: 10.1103/PhysRevB.72.180403
[32]	White S R 1996 Phys. Rev. Lett. 77 3633 doi: 10.1103/PhysRevLett.77.3633
[33]	Stoudenmire E M and White S R 2013 Phys. Rev. B 87 155137 doi: 10.1103/PhysRevB.87.155137
[34]	Hager G, Jeckelmann E, Fehske H and Wellein G 2004 J. Comput. Phys. 194 795 doi: 10.1016/j.jcp.2003.09.018
[35]	Romero E and Roman J E 2014 ACM Trans. Math. Software 40 13:1
[36]	Nemes C, Barcza G, Nagy Z, Legeza O and Szolgay P 2014 Comput. Phys. Commun. 185 1570 doi: 10.1016/j.cpc.2014.02.021
[37]	Chen F Z, Cheng C and Luo H G 2019 Acta Phys. Sin. 68 120202 (in Chinese)
[38]	Intel 2019 Intel Math Kernel Library Developer Reference
[39]	NVIDIA 2018 CUBLAS Library v. 9.2
[40]	OpenMP Application Programming Interface
[41]	Davidson E R 1975 J. Comput. Phys. 17 87 doi: 10.1016/0021-9991(75)90065-0
[42]	Matrix Algebra on GPU and Multicore Architectures (MAGMA), http://icl.cs.utk.edu/magma/
[43]	ITensor Library (version 3.1.0)

Improved hybrid parallel strategy for density matrix renormalization group method

Improved hybrid parallel strategy for density matrix renormalization group method

RichHTML

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献 43

相关文章 3

Metrics

本文评价

推荐阅读 0

[1]	Fu-Zhou Chen(陈富州), Chen Cheng(程晨), and Hong-Gang Luo(罗洪刚). Real-space parallel density matrix renormalization group with adaptive boundaries[J]. 中国物理B, 2021, 30(8): 80202-080202.
[2]	Cong Fu(傅聪), Hui Zhao(赵晖), Yu-Guang Chen(陈宇光), and Yong-Hong Yan(鄢永红). Ground-state phase diagram of the dimerizedspin-1/2 two-leg ladder[J]. 中国物理B, 2021, 30(8): 87501-087501.
[3]	范二女, 张万舟. Off-site trimer superfluid on a one-dimensional optical lattice[J]. 中国物理B, 2017, 26(4): 43701-043701.