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Chin. Phys. B, 2020, Vol. 29(7): 070202    DOI: 10.1088/1674-1056/ab8a42
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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
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.
Keywords:  density matrix renormalization group      strongly correlated model      hybrid parallelization  
Received:  21 January 2020      Revised:  07 April 2020      Accepted manuscript online: 
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 University, 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), Hong-Gang Luo(罗洪刚) Improved hybrid parallel strategy for density matrix renormalization group method 2020 Chin. Phys. B 29 070202

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