Real-space parallel density matrix renormalization group with adaptive boundaries*

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.

Finite-temperature optical conductivity with density-matrix renormalization group methods for the Holstein polaron and bipolaron with dispersive phonons

“…Therefore, a need for dynamically adapting the boundaries as suggested for pDMRG in Ref. [137] does not seem necessary for our applications.…”

Low communication high performance ab initio density matrix renormalization group algorithms

“…A more recent approach to coarse-grained parallelism in DMRG is the "real space parallel DMRG" approach introduced by Stoudenmire and White, 34,48 which has been shown to give near ideal scaling in some calculations with model Hamiltonians and very recently for quantum chemistry Hamiltonian. 49 An implementation of this approach for (non-spin-adapted) quantum chemistry Hamiltonians can also be found in the QCMaquis code. 40 The approach relies on a representation of the MPS with multiple canonical centers.…”

“…If the same number of sites is assigned to different processors, one observes a significant load imbalance, which negatively impacts the scalability. 49 To alleviate this problem, similar to the dynamic boundary strategy used in Ref. 49, we have added an additional step to dynamically determine the position of the canonical center (connection site) to improve load balancing.…”

“…49 To alleviate this problem, similar to the dynamic boundary strategy used in Ref. 49, we have added an additional step to dynamically determine the position of the canonical center (connection site) to improve load balancing. After all processors finish their partial sweeps, the total computational cost is measured for each processor for the partial sweep and all its sweep iterations.…”

“…In contrast, the approach introduced in Ref. 49 completely removes the waiting time at each sweep, but introduces an extra projection error in the wavefunction initial guess (Eq. ( 10)) when the connection site is changed (which is larger for ab initio systems compared to spin systems, according to Ref.…”