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

Area of Science:

• Quantum Chemistry
• Computational Physics
• Theoretical Chemistry

Background:

• The three-legged tree tensor network state (T3NS) offers a balance between computational efficiency and entanglement representation.
• Existing T3NS methods have limitations in fully exploiting certain symmetries.

Purpose of the Study:

• To extend the T3NS formalism by integrating spin and real abelian point group symmetries.
• To improve the accuracy and reduce the computational cost of quantum chemical calculations using T3NS.

Main Methods:

• Interspersing physical tensors (one physical, <=2 virtual indices) with branching tensors (up to 3 virtual indices).
• Incorporating spin and real abelian point group symmetries into the T3NS structure.
• Applying the enhanced T3NS to model systems like [Cu2O2]2+ isomers.

Main Results:

• Demonstrated improved accuracy in calculations for bis(μ-oxo) and μ-η2:η2 peroxo isomers of [Cu2O2]2+.
• Achieved these more accurate results with lower computational effort compared to previous methods.
• The enhanced T3NS effectively represents entanglement while leveraging symmetry properties.

Conclusions:

• The integration of spin and point group symmetries significantly enhances the capabilities of T3NS.
• This advancement leads to more efficient and accurate quantum chemical computations.
• The developed implementation is publicly available for further research.