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• W1796314718 abstract "We present the Copupled Cluster (CC) method and the Density matrix Renormalization Grooup (DMRG) method in a unified way, from the perspective of recent developments in tensor product approximation. We present an introduction into recently developed hierarchical tensor representations, in particular tensor trains which are matrix product states in physics language. The discrete equations of full CI approximation applied to the electronic Schrodinger equation is casted into a tensorial framework in form of the second quantization. A further approximation is performed afterwards by tensor approximation within a hierarchical format or equivalently a tree tensor network. We establish the (differential) geometry of low rank hierarchical tensors and apply the Driac Frenkel principle to reduce the original high-dimensional problem to low dimensions. The DMRG algorithm is established as an optimization method in this format with alternating directional search. We briefly introduce the CC method and refer to our theoretical results. We compare this approach in the present discrete formulation with the CC method and its underlying exponential parametrization." @default.
• W1796314718 created "2016-06-24" @default.
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• W1796314718 date "2014-01-01" @default.
• W1796314718 modified "2023-10-03" @default.
• W1796314718 title "Tensor Product Approximation (DMRG) and Coupled Cluster Method in Quantum Chemistry" @default.
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• W1796314718 doi "https://doi.org/10.1007/978-3-319-06379-9_3" @default.
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