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The Density Matrix Renormalization Group (DMRG) algorithm is a powerful toolfor solving eigenvalue problems to model quantum systems. DMRG relies on tensorcontractions and dense linear algebra to compute properties of condensed matterphysics systems. However, its efficient parallel implementation is challengingdue to limited concurrency, large memory footprint, and tensor sparsity. Wemitigate these problems by implementing two new parallel approaches that handleblock sparsity arising in DMRG, via Cyclops, a distributed memory tensorcontraction library. We benchmark their performance on two physical systemsusing the Blue Waters and Stampede2 supercomputers. Our DMRG performance isimproved by up to 5.9X in runtime and 99X in processing rate over ITensor, atroughly comparable computational resource use. This enables higher accuracycalculations via larger tensors for quantum state approximation. We demonstratethat despite having limited concurrency, DMRG is weakly scalable with the useof efficient parallel tensor contraction mechanisms.

Distributed-Memory DMRG via Sparse and Dense Parallel Tensor Contractions