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Three-Legged Tree Tensor Networks with SU(2) and Molecular Point Group Symmetry

Klaas Gunst (UGent) , Frank Verstraete (UGent) and Dimitri Van Neck (UGent)
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Abstract
We extend the three-legged tree tensor network state (T3NS) [J. Chem. Theory Comput. 2018, 14, 2026-2033] by including spin and the real abelian point group symmetries. T3NS intersperses physical tensors with branching tensors. Physical tensors have one physical index and at most two virtual indices. Branching tensors have up to three virtual indices and no physical index. In this way, T3NS combines the low computational cost of matrix product states and their simplicity for implementing symmetries, with the better entanglement representation of tree tensor networks. By including spin and point group symmetries, more accurate calculations can be obtained with lower computational effort. We illustrate this by presenting calculations on the bis(mu-oxo) and mu-eta(2):eta(2) peroxo isomers of [Cu2O2](2+). The used implementation is available on github.
Keywords
MATRIX RENORMALIZATION-GROUP

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Chicago
Gunst, Klaas, Frank Verstraete, and Dimitri Van Neck. 2019. “Three-Legged Tree Tensor Networks with SU(2) and Molecular Point Group Symmetry.” Journal of Chemical Theory and Computation 15 (5): 2996–3007.
APA
Gunst, K., Verstraete, F., & Van Neck, D. (2019). Three-Legged Tree Tensor Networks with SU(2) and Molecular Point Group Symmetry. JOURNAL OF CHEMICAL THEORY AND COMPUTATION, 15(5), 2996–3007.
Vancouver
1.
Gunst K, Verstraete F, Van Neck D. Three-Legged Tree Tensor Networks with SU(2) and Molecular Point Group Symmetry. JOURNAL OF CHEMICAL THEORY AND COMPUTATION. Washington: Amer Chemical Soc; 2019;15(5):2996–3007.
MLA
Gunst, Klaas, Frank Verstraete, and Dimitri Van Neck. “Three-Legged Tree Tensor Networks with SU(2) and Molecular Point Group Symmetry.” JOURNAL OF CHEMICAL THEORY AND COMPUTATION 15.5 (2019): 2996–3007. Print.
@article{8618769,
  abstract     = {We extend the three-legged tree tensor network state (T3NS) [J. Chem. Theory Comput. 2018, 14, 2026-2033] by including spin and the real abelian point group symmetries. T3NS intersperses physical tensors with branching tensors. Physical tensors have one physical index and at most two virtual indices. Branching tensors have up to three virtual indices and no physical index. In this way, T3NS combines the low computational cost of matrix product states and their simplicity for implementing symmetries, with the better entanglement representation of tree tensor networks. By including spin and point group symmetries, more accurate calculations can be obtained with lower computational effort. We illustrate this by presenting calculations on the bis(mu-oxo) and mu-eta(2):eta(2) peroxo isomers of [Cu2O2](2+). The used implementation is available on github.},
  author       = {Gunst, Klaas and Verstraete, Frank and Van Neck, Dimitri},
  issn         = {1549-9618},
  journal      = {JOURNAL OF CHEMICAL THEORY AND COMPUTATION},
  keywords     = {MATRIX RENORMALIZATION-GROUP},
  language     = {eng},
  number       = {5},
  pages        = {2996--3007},
  publisher    = {Amer Chemical Soc},
  title        = {Three-Legged Tree Tensor Networks with SU(2) and Molecular Point Group Symmetry},
  url          = {http://dx.doi.org/10.1021/acs.jctc.9b00071},
  volume       = {15},
  year         = {2019},
}

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