Low communication high performance ab initio density matrix renormalization group algorithms

Area of Science:

• Computational Chemistry
• Quantum Physics
• High-Performance Computing

Background:

• Recent interest in deploying ab initio Density Matrix Renormalization Group (DMRG) computations on high-performance computing (HPC) platforms.
• Conventional distributed memory ab initio DMRG algorithms face challenges in efficiency and scalability.

Purpose of the Study:

• To introduce a reformulated ab initio DMRG algorithm.
• To connect the conventional algorithm to the sum of the sub-Hamiltonian approach for improved conceptual simplicity and performance.
• To explore and implement a hierarchy of parallelism strategies.

Main Methods:

• Reformulation of the conventional distributed memory ab initio DMRG algorithm.
• Integration with the sum of the sub-Hamiltonian approach.
• Implementation of parallelism strategies: sum of sub-Hamiltonians, sites, operators, symmetry sectors, and dense matrix multiplications.
• Techniques to reduce processor load imbalance and communication costs.

Main Results:

• Demonstration of an open-source implementation of the reformulated algorithm.
• Performance illustration on benchmark calculations: benzene (108 orbitals, 30 electrons, bond dimension 6000) and FeMo cofactor (76 orbitals, 113 electrons).
• Observed nearly ideal parallel scaling from 448 to 2800 CPU cores.

Conclusions:

• The reformulated ab initio DMRG algorithm offers significant efficiency improvements on HPC platforms.
• The sum of the sub-Hamiltonian approach provides a conceptually simpler and advantageous framework.
• The implemented parallelism strategies and load balancing techniques lead to high parallel efficiency for large-scale quantum chemical problems.