T3NS: Three-Legged Tree Tensor Network States.

Area of Science:

• Quantum Many-Body Physics
• Computational Chemistry
• Tensor Network States

Background:

• Matrix Product States (MPS) and Density Matrix Renormalization Group (DMRG) offer efficient simulations but have limitations in capturing high entanglement.
• Tree Tensor Networks (TTNS) can incorporate more entanglement but often come with increased computational complexity.
• Simulating complex quantum chemical systems requires advanced computational methods that balance accuracy and efficiency.

Purpose of the Study:

• To introduce a novel variational tensor network state, the three-legged tree tensor network state (T3NS).
• To combine the computational advantages of DMRG with the entanglement handling capabilities of TTNS.
• To develop and apply a computational code for simulating quantum chemical Hamiltonians using the T3NS ansatz.

Main Methods:

• Developed a new variational ansatz: the three-legged tree tensor network state (T3NS).
• Incorporated physical tensors (one physical, up to two virtual indices) and branching tensors (no physical, up to three virtual indices).
• Implemented a computational code capable of simulating quantum chemical Hamiltonians.

Main Results:

• The T3NS ansatz successfully combines the low computational cost and symmetry implementation of DMRG with the enhanced entanglement description of TTNS.
• Proof-of-principle calculations were performed on various quantum chemical systems.
• Simulations included LiF, N₂, and the bis(μ-oxo) and μ-η²:η² peroxo isomers of [Cu₂O₂]²⁺.

Conclusions:

• The T3NS ansatz represents a promising advancement in tensor network methods for quantum many-body problems.
• This new method offers a powerful tool for accurate and efficient simulations of complex quantum chemical systems.
• The developed code provides a practical implementation for exploring strongly correlated electronic structures.