Please wait a minute...
Chin. Phys. B, 2021, Vol. 30(8): 080202    DOI: 10.1088/1674-1056/abeb08
GENERAL Prev   Next  

Real-space parallel density matrix renormalization group with adaptive boundaries

Fu-Zhou Chen(陈富州)1, Chen Cheng(程晨)1, and 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
Abstract  We propose an improved real-space parallel strategy for the density matrix renormalization group (DMRG) method, where boundaries of separate regions are adaptively distributed during DMRG sweeps. Our scheme greatly improves the parallel efficiency with shorter waiting time between two adjacent tasks, compared with the original real-space parallel DMRG with fixed boundaries. We implement our new strategy based on the message passing interface (MPI), and dynamically control the number of kept states according to the truncation error in each DMRG step. We study the performance of the new parallel strategy by calculating the ground state of a spin-cluster chain and a quantum chemical Hamiltonian of the water molecule. The maximum parallel efficiencies for these two models are 91% and 76% in 4 nodes, which are much higher than the real-space parallel DMRG with fixed boundaries.
Keywords:  density matrix renormalization group      strongly correlated systems      message passing interface  
Received:  30 November 2020      Revised:  10 February 2021      Accepted manuscript online:  02 March 2021
PACS:  02.70.-c (Computational techniques; simulations)  
  71.10.Fd (Lattice fermion models (Hubbard model, etc.))  
  71.27.+a (Strongly correlated electron systems; heavy fermions)  
  05.10.Cc (Renormalization group methods)  
Fund: 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 Universities, China (Grant No. IRT-16R35).
Corresponding Authors:  Hong-Gang Luo     E-mail:

Cite this article: 

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 2021 Chin. Phys. B 30 080202

[1] White S R 1992 Phys. Rev. Lett. 69 2863
[2] White S R 1993 Phys. Rev. B 48 10345
[3] Verstraete F, Porras D and Cirac J I 2004 Phys. Rev. Lett. 93 227205
[4] Schollwöck U 2011 Ann. Phys. 326 96
[5] Cheng C, Mao B B, Chen F Z and Luo H G 2015 Europhys. Lett. 110 37002
[6] Cheng C, Mao B B, Chen F Z and Luo H G 2015 Eur. Phys. J. B 88 152
[7] Bravo B, Cabra D C, Gómez Albarracín F A and Rossini G L 2017 Phys. Rev. B 96 054441
[8] Dür W, Hartmann L, Hein M, Lewenstein M and Briegel H J 2005 Phys. Rev. Lett. 94 097203
[9] White S R and Scalapino D J 2003 Phys. Rev. Lett. 91 136403
[10] Ramos F B and Xavier J C 2014 Phys. Rev. B 89 094424
[11] Cheng C, Mondaini R and Rigol M 2018 Phys. Rev. B 98 121112
[12] White S R and Chernyshev A L 2007 Phys. Rev. Lett. 99 127004
[13] Depenbrock S, McCulloch I P and Schollwöck U 2012 Phys. Rev. Lett. 109 067201
[14] Stoudenmire E M and White S R 2012 Ann. Rev. Condens. Matter Phys. 3 111
[15] 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
[16] Wang L and Sandvik A W 2018 Phys. Rev. Lett. 121 107202
[17] Yu W C, Cheng C and Sacramento P D 2020 Phys. Rev. B 101 245131
[18] Xiang T 1996 Phys. Rev. B 53 R10445
[19] Motruk J, Zaletel M P, Mong R S K and Pollmann F 2016 Phys. Rev. B 93 155139
[20] Ehlers G, White S R and Noack R M 2017 Phys. Rev. B 95 125125
[21] White S R and Martin R L 1999 J. Chem. Phys. 110 4127
[22] Chan G K L and Sharma S 2011 Ann. Rev. Phys. Chem. 62 465
[23] Baiardi A and Reiher M 2020 J. Chem. Phys. 152 040903
[24] Luo H G, Qin M P and Xiang T 2010 Phys. Rev. B 81 235129
[25] Alvarez G 2010 Comput. Phys. Commun. 180 1572
[26] Tzeng Y C 2012 Phys. Rev. B 86 024403
[27] White S R 1996 Phys. Rev. Lett. 77 3633
[28] Legeza O, Röder J and Hess B A 2003 Phys. Rev. B 67 125114
[29] Legeza O and Sólyom J 2003 Phys. Rev. B 68 195116
[30] White S R 2005 Phys. Rev. B 72 180403
[31] Hubig C, McCulloch I P, Schollwöck U and Wolf F A 2015 Phys. Rev. B 91 155115
[32] Núñez Fernández Y and Torroba G 2020 Phys. Rev. B 101 085135
[33] Kurashige Y and Yanai T 2009 J. Chem. Phys. 130 234114
[34] Chan G K L 2004 J. Chem. Phys. 120 3172
[35] Hager G, Jeckelmann E, Fehske H and Wellein G 2004 J. Comput. Phys. 194 795
[36] Nemes C, Barcza G, Nagy Z, Legeza O and Szolgay P 2014 Comput. Phys. Commun. 185 1570
[37] Chen F Z, Cheng C and Luo H G 2019 Acta Phys. Sin. 68 120202 (in Chinese)
[38] Chen F Z, Cheng C and Luo H G 2020 Chin. Phys. B 29 070202
[39] Stoudenmire E M and White S R 2013 Phys. Rev. B 87 155137
[40] Ueda H 2018 J. Phys. Soc. Jpn. 87 074005
[41] Urbanek M and Soldán P 2016 Comput. Phys. Commun. 199 170
[42] Secular P, Gourianov N, Lubasch M, Dolgov S, Clark S R and Jaksch D 2020 Phys. Rev. B 101 235123
[43] Starova G L, Filatov S K, Fundamensky V S and Vergasova L P 1991 Mineralog. Mag. 55 613
[44] Fujihala M, Sugimoto T, Tohyama T, Mitsuda S, Mole R A, Yu D H, Yano S, Inagaki Y, Morodomi H, Kawae T, Sagayama H, Kumai R, Murakami Y, Tomiyasu K, Matsuo A and Kindo K 2018 Phys. Rev. Lett. 120 077201
[45] Hase M, Rule K C, Hester J R, Fernandez-Baca J A, Masuda T and Matsuo Y 2019 J. Phys. Soc. Jpn. 88 094708
[46] Zhou Z, Chen F, Zhong Y, Luo H G and Zhao J 2019 Phys. Rev. B 99 205143
[47] Furrer A, Podlesnyak A, Clemente-Juan J M, Pomjakushina E and Güdel H U 2020 Phys. Rev. B 101 224417
[48] Chan G K L and Head-Gordon M 2003 J. Chem. Phys. 118 8551
[49] Hachmann J, Cardoen W and Chan G K L 2006 J. Chem. Phys. 125 144101
[50] Marti K H, Ondík I M, Moritz G and Reiher M 2008 J. Chem. Phys. 128 014104
[51] Sharma S, Sivalingam K, Neese F and Chan G K L 2014 Nat. Chem. 6 927
[52] Knecht S, Legeza O and Reiher M 2014 J. Chem. Phys. 140 041101
[53] Smith D G A, Burns L A, Simmonett A C, Parrish R M, Schieber M C, Galvelis R, Kraus P, Kruse H, Di Remigio R, Alenaizan A, James A M, Lehtola S, Misiewicz J P, Scheurer M, Shaw R A, Schriber J B, Xie Y, Glick Z L, Sirianni D A, O'Brien J S, Waldrop J M, Kumar A, Hohenstein E G, Pritchard B P, Brooks B R, Schaefer H F, Sokolov A Y, Patkowski K, DePrince A E, Bozkaya U, King R A, Evangelista F A, Turney J M, Crawford T D and Sherrill C D 2020 J. Chem. Phys. 152 184108
[54] Fishman M, White S R and Miles Stoudenmire E 2020 arXiv:2007.14822 [cs.MS]
[55] Wouters S, Poelmans W, Ayers P W and Neck D V 2014 Comput. Phys. Commun. 185 1501
[56] Chan G K L and Head-Gordon M 2002 J. Chem. Phys. 116 4462
[57] Moritz G, Hess B A and Reiher M 2005 J. Chem. Phys. 122 024107
[58] Rissler J, Noack R M and White S R 2006 Chem. Phys. 323 519
[59] White S R and Feiguin A E 2004 Phys. Rev. Lett. 93 076401
[60] Haegeman J, Cirac J I, Osborne T J, Pižorn I, Verschelde H and Verstraete F 2011 Phys. Rev. Lett. 107 070601
[1] Ground-state phase diagram of the dimerizedspin-1/2 two-leg ladder
Cong Fu(傅聪), Hui Zhao(赵晖), Yu-Guang Chen(陈宇光), and Yong-Hong Yan(鄢永红). Chin. Phys. B, 2021, 30(8): 087501.
[2] Equilibrium dynamics of the sub-ohmic spin-boson model at finite temperature
Ke Yang(杨珂) and Ning-Hua Tong(同宁华). Chin. Phys. B, 2021, 30(4): 040501.
[3] Relevance of 3d multiplet structure in nickelate and cuprate superconductors
Mi Jiang(蒋密). Chin. Phys. B, 2021, 30(10): 107103.
[4] Coupling analysis of transmission lines excited by space electromagnetic fields based on time domain hybrid method using parallel technique
Zhi-Hong Ye(叶志红), Xiao-Lin Wu(吴小林), Yao-Yao Li(李尧尧). Chin. Phys. B, 2020, 29(9): 090701.
[5] 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). Chin. Phys. B, 2020, 29(7): 070202.
[6] Off-site trimer superfluid on a one-dimensional optical lattice
Er-Nv Fan(范二女), Tony C Scott, Wan-Zhou Zhang(张万舟). Chin. Phys. B, 2017, 26(4): 043701.
No Suggested Reading articles found!