Efficient electronic structure theory via hierarchical scale-adaptive coupled-cluster formalism: I. Theory and computational complexity analysis

A novel reduced-scaling, general-order coupled-cluster approach is formulated by exploiting hierarchical representations of many-body tensors, combined with the recently suggested formalism of scale-adaptive tensor algebra. Inspired by the hierarchical techniques from the renormalisation group appro...

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Veröffentlicht in:Molecular physics Jg. 116; H. 5-6; S. 588 - 601
1. Verfasser: Lyakh, Dmitry I.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Abingdon Taylor & Francis 19.03.2018
Taylor & Francis Ltd
Schlagworte:
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
Clusters
Coarsening
Complexity
Computation
Computer simulation
coupled-cluster
Electronic structure
Euclidean geometry
Floating point arithmetic
Floating structures
Formalism
Hierarchical tensor
linear scaling
Many body interactions
Mathematical analysis
MATHEMATICS AND COMPUTING
Matrix algebra
Scaling
Structural hierarchy
Tensors
ISSN:0026-8976, 1362-3028
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Zusammenfassung:A novel reduced-scaling, general-order coupled-cluster approach is formulated by exploiting hierarchical representations of many-body tensors, combined with the recently suggested formalism of scale-adaptive tensor algebra. Inspired by the hierarchical techniques from the renormalisation group approach, H/H 2 -matrix algebra and fast multipole method, the computational scaling reduction in our formalism is achieved via coarsening of quantum many-body interactions at larger interaction scales, thus imposing a hierarchical structure on many-body tensors of coupled-cluster theory. In our approach, the interaction scale can be defined on any appropriate Euclidean domain (spatial domain, momentum-space domain, energy domain, etc.). We show that the hierarchically resolved many-body tensors can reduce the storage requirements to O(N), where N is the number of simulated quantum particles. Subsequently, we prove that any connected many-body diagram consisting of a finite number of arbitrary-order tensors, e.g. an arbitrary coupled-cluster diagram, can be evaluated in O(NlogN) floating-point operations. On top of that, we suggest an additional approximation to further reduce the computational complexity of higher order coupled-cluster equations, i.e. equations involving higher than double excitations, which otherwise would introduce a large prefactor into formal O(NlogN) scaling.
Bibliographie:ObjectType-Article-1
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content type line 14
USDOE Office of Science (SC)
AC05-00OR22725
ISSN:0026-8976
1362-3028
DOI:10.1080/00268976.2017.1367856