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.

arXiv comment20 pages, 13 figures

References in corpus (34)

• Entanglement renormalization
• Thermodynamic limit of the density matrix renormalization for the spin-1 Heisenberg chain
• Classical simulation of quantum many-body systems with a tree tensor network
• Ab Initio Quantum Chemistry using the Density Matrix Renormalization Group
• Renormalization algorithms for Quantum-Many Body Systems in two and higher dimensions
• From density-matrix renormalization group to matrix product states
• A class of ansatz wave functions for 1D spin systems and their relation to DMRG
• 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 product methods and entanglement optimization for ab initio quantum chemistry
• Tensor network states and algorithms in the presence of a global U(1) symmetry
• Tensor network decompositions in the presence of a global symmetry
• A spin-adapted Density Matrix Renormalization Group algorithm for quantum chemistry
• Non-abelian symmetries in tensor networks: a quantum symmetry space approach
• Controlling the accuracy of the density matrix renormalization group method: The Dynamical Block State Selection approach
• Simulating Strongly Correlated Quantum Systems with Tree Tensor Networks
• The Non-Abelian Density Matrix Renormalization Group Algorithm
• Quantum information analysis of electronic states at different molecular structures
• CheMPS2: a free open-source spin-adapted implementation of the density matrix renormalization group for ab initio quantum chemistry
• Efficient Tree Tensor Network States (TTNS) for Quantum Chemistry: Generalizations of the Density Matrix Renormalization Group Algorithm
• Isometric Tensor Network States in Two Dimensions
• Tensor network states and algorithms in the presence of a global SU(2) symmetry
• Coupled cluster method with single and double excitations tailored by matrix product state wave functions
• 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
• DMRG-CASPT2 study of the longitudinal static second hyperpolarizability of all-trans polyenes
• Gauge fixing, canonical forms and optimal truncations in tensor networks with closed loops
• T3NS: three-legged tree tensor network states
• Matrix product decomposition and classical simulation of quantum dynamics in the presence of a symmetry
• The area law and real-space renormalization
• Abelian and non-abelian symmetries in infinite projected entangled pair states
• Self-Adaptive Tensor Network States with Multi-Site Correlators

Cited by in corpus (8)

• Restricted Boltzmann Machines for Quantum States with Nonabelian or Anyonic Symmetries
• Automatic structural optimization of tree tensor networks
• Many-Body Quantum States with Exact Conservation of Non-Abelian and Lattice Symmetries through Variational Monte Carlo
• Expressibility of comb tensor network states (CTNS) for the P-cluster and the FeMo-cofactor of nitrogenase
• Quantum Quench and Charge Oscillations in the SU(3) Hubbard Model: a Test of Time Evolving Block Decimation with general non-Abelian Symmetries
• Two dimensional quantum lattice models via mode optimized hybrid CPU-GPU density matrix renormalization group method
• The seniority quantum number in Tensor Network States
• Hierarchical Search of Tree Tensor Networks for High-Dimensional Data