SciPost Phys. Core 7, 002 (2024) ·
published 22 January 2024

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We demonstrate that in Weyl semimetals, the momentumspace helical spin texture can couple to the chirality of the Weyl node to generate a frequencyindependent optical spin injection. This frequencyindependence is rooted in the topology of the Weyl node. Since the helicity and the chirality are always locked for Weyl nodes, the injected spin from a pair of Weyl nodes always add up, implying no symmetry requirements for Weyl semimetals. Finally, we show that such frequencyindependent spin injection is robust against multiband corrections and latticeregularization effect and capable of realizing alloptical magnetization switching in the THz regime.
Yang Gao, Phillip Helms, Garnet KinLic Chan, Edgar Solomonik
SciPost Phys. Codebases 10 (2023) ·
published 24 February 2023

· pdf
Tensor contractions are ubiquitous in computational chemistry and physics, where tensors generally represent states or operators and contractions express the algebra of these quantities. In this context, the states and operators often preserve physical conservation laws, which are manifested as group symmetries in the tensors. These group symmetries imply that each tensor has block sparsity and can be stored in a reduced form. For nontrivial contractions, the memory footprint and cost are lowered, respectively, by a linear and a quadratic factor in the number of symmetry sectors. Stateoftheart tensor contraction software libraries exploit this opportunity by iterating over blocks or using general blocksparse tensor representations. Both approaches entail overhead in performance and code complexity. With intuition aided by tensor diagrams, we present a technique, irreducible representation alignment, which enables efficient handling of Abelian group symmetries via only dense tensors, by using contractionspecific reduced forms. This technique yields a general algorithm for arbitrary group symmetric contractions, which we implement in Python and apply to a variety of representative contractions from quantum chemistry and tensor network methods. As a consequence of relying on only dense tensor contractions, we can easily make use of efficient batched matrix multiplication via Intel's MKL and distributed tensor contraction via the Cyclops library, achieving good efficiency and parallel scalability on up to 4096 Knights Landing cores of a supercomputer.
Yang Gao, Phillip Helms, Garnet KinLic Chan, Edgar Solomonik
SciPost Phys. Codebases 10r1.3 (2023) ·
published 24 February 2023

· src
Tensor contractions are ubiquitous in computational chemistry and physics, where tensors generally represent states or operators and contractions express the algebra of these quantities. In this context, the states and operators often preserve physical conservation laws, which are manifested as group symmetries in the tensors. These group symmetries imply that each tensor has block sparsity and can be stored in a reduced form. For nontrivial contractions, the memory footprint and cost are lowered, respectively, by a linear and a quadratic factor in the number of symmetry sectors. Stateoftheart tensor contraction software libraries exploit this opportunity by iterating over blocks or using general blocksparse tensor representations. Both approaches entail overhead in performance and code complexity. With intuition aided by tensor diagrams, we present a technique, irreducible representation alignment, which enables efficient handling of Abelian group symmetries via only dense tensors, by using contractionspecific reduced forms. This technique yields a general algorithm for arbitrary group symmetric contractions, which we implement in Python and apply to a variety of representative contractions from quantum chemistry and tensor network methods. As a consequence of relying on only dense tensor contractions, we can easily make use of efficient batched matrix multiplication via Intel's MKL and distributed tensor contraction via the Cyclops library, achieving good efficiency and parallel scalability on up to 4096 Knights Landing cores of a supercomputer.