Distributed-Memory DMRG via Sparse and Dense Parallel Tensor Contractions

Abstract

The Density Matrix Renormalization Group (DMRG) algorithm is a powerful tool for solving eigenvalue problems to model quantum systems. DMRG relies on tensor contractions and dense linear algebra to compute properties of condensed matter physics systems. However, its efficient parallel implementation is challenging due to limited concurrency, large memory footprint, and tensor sparsity. We mitigate these problems by implementing two new parallel approaches that handle block sparsity arising in DMRG, via Cyclops, a distributed memory tensor contraction library. We benchmark their performance on two physical systems using the Blue Waters and Stampede2 supercomputers. Our DMRG performance is improved by up to 5.9X in runtime and 99X in processing rate over ITensor, at roughly comparable computational resource use. This enables higher accuracy calculations via larger tensors for quantum state approximation. We demonstrate that despite having limited concurrency, DMRG is weakly scalable with the use of efficient parallel tensor contraction mechanisms.

References in corpus (15)

• Thermodynamic limit of the density matrix renormalization for the spin-1 Heisenberg chain
• Critical level crossings and gapless spin liquid in the square-lattice spin-$1/2$ $J_1$-$J_2$ Heisenberg antiferromagnet
• Advances on Tensor Network Theory: Symmetries, Fermions, Entanglement, and Holography
• Format Abstraction for Sparse Tensor Algebra Compilers
• Matrix Product State applications for the ALPS project
• Real-Space Parallel Density Matrix Renormalization Group
• Ground state phase diagram of the triangular lattice Hubbard model by density matrix renormalization group method
• $U(1)$-symmetric infinite projected entangled-pair state study of the spin-$1/2$ square $J_1-J_2$ Heisenberg model
• Quantum critical phase with infinite projected entangled paired states
• Gapless spin liquid ground state of spin-1/2 $J_1$-$J_2$ Heisenberg model on square lattices
• Understanding repulsively mediated superconductivity of correlated electrons via massively parallel DMRG
• Improved parallelization techniques for the density matrix renormalization group
• On Stability of Tensor Networks and Canonical Forms
• Infinite-size density matrix renormalization group with parallel Hida's algorithm
• DBCSR: A Blocked Sparse Tensor Algebra Library

Cited by in corpus (3)

• Block2: a comprehensive open source framework to develop and apply state-of-the-art DMRG algorithms in electronic structure and beyond
• Low communication high performance ab initio density matrix renormalization group algorithms
• Performance of the rigorous renormalization group for first order phase transitions and topological phases