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Efficient tree tensor network states (TTNS) for quantum chemistry: Generalizations of the density matrix renormalization group algorithm

Nakatani, Naoki and Chan, Garnet Kin-Lic (2013) Efficient tree tensor network states (TTNS) for quantum chemistry: Generalizations of the density matrix renormalization group algorithm. Journal of Chemical Physics, 138 (13). Art. No. 134113. ISSN 0021-9606. doi:10.1063/1.4798639.

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We investigate tree tensor network states for quantum chemistry. Tree tensor network states represent one of the simplest generalizations of matrix product states and the density matrix renormalization group. While matrix product states encode a one-dimensional entanglement structure, tree tensor network states encode a tree entanglement structure, allowing for a more flexible description of general molecules. We describe an optimal tree tensor network state algorithm for quantum chemistry. We introduce the concept of half-renormalization which greatly improves the efficiency of the calculations. Using our efficient formulation we demonstrate the strengths and weaknesses of tree tensor network states versus matrix product states. We carry out benchmark calculations both on tree systems (hydrogen trees and π-conjugated dendrimers) as well as non-tree molecules (hydrogen chains, nitrogen dimer, and chromium dimer). In general, tree tensor network states require much fewer renormalized states to achieve the same accuracy as matrix product states. In non-tree molecules, whether this translates into a computational savings is system dependent, due to the higher prefactor and computational scaling associated with tree algorithms. In tree like molecules, tree network states are easily superior to matrix product states. As an illustration, our largest dendrimer calculation with tree tensor network states correlates 110 electrons in 110 active orbitals.

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Chan, Garnet Kin-Lic0000-0001-8009-6038
Additional Information:© 2013 American Institute of Physics. Received 30 January 2013; accepted 14 March 2013; published online 4 April 2013. This work was supported by the National Science Foundation (NSF) through Grant No. NSF-OCI-1148287 and NSF-CHE-1213933.
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Issue or Number:13
Record Number:CaltechAUTHORS:20170126-084951680
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:73748
Deposited By: Donna Wrublewski
Deposited On:26 Jan 2017 17:07
Last Modified:11 Nov 2021 05:21

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