The Three-Legged Tree Tensor Networks with SU(2)- and molecular point group symmetry

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 $[{\mathrm{Cu}}_2{\mathrm{O}}_2{]}^{2+}$. The used implementation is available on github.

20 pages, 13 figures

References in corpus (14)

• Renormalization algorithms for Quantum-Many Body Systems in two and higher dimensions
• From density-matrix renormalization group to matrix product states
• Orbital Optimization in the Density Matrix Renormalization Group, with applications to polyenes and β-carotene
• The density matrix renormalization group for ab initio quantum chemistry
• Tensor network states and algorithms in the presence of a global U(1) symmetry
• A spin-adapted Density Matrix Renormalization Group algorithm for quantum chemistry
• Simulating Strongly Correlated Quantum Systems with Tree Tensor Networks
• Efficient Tree Tensor Network States (TTNS) for Quantum Chemistry: Generalizations of the Density Matrix Renormalization Group Algorithm
• Fermionic Matrix Product States and One-Dimensional Topological Phases
• DMRG-SCF study of the singlet, triplet, and quintet states of oxo-Mn(Salen)
• Complete-Graph Tensor Network States: A New Fermionic Wave Function Ansatz for Molecules
• Density matrix numerical renormalization group for non-Abelian symmetries
• The area law and real-space renormalization
• Self-Adaptive Tensor Network States with Multi-Site Correlators