Fine Grained Tensor Network Methods.

Area of Science:

• Quantum physics
• Computational condensed matter physics

Background:

• Tensor network algorithms are powerful tools for simulating quantum many-body systems.
• Simulating systems on lattices with high connectivity poses significant computational challenges.
• Existing methods struggle with complex lattice structures, limiting their applicability.

Purpose of the Study:

• To develop an efficient tensor network algorithm strategy for simulating systems on high-connectivity lattices.
• To simplify complex lattice structures for easier simulation using standard tensor network techniques.
• To enable the application of established contraction schemes, like corner transfer matrix renormalization, to intricate lattice geometries.

Main Methods:

• A novel strategy involving fine-graining physical degrees of freedom.
• Decomposition of degrees of freedom into fundamental units followed by coarse-graining.
• Transformation of high-connectivity lattices into simpler structures via isometries.
• Numerical computation of ground-state properties using the developed method.

Main Results:

• Successfully computed ground-state properties for the spin-1 transverse-field Ising model on 2D and 3D triangular lattices.
• Calculated properties for hardcore and softcore Bose-Hubbard models on the triangular lattice.
• Achieved excellent agreement with results from perturbative continuous unitary transformations and graph projected entangled pair states.
• Demonstrated improved performance in several simulation regimes.

Conclusions:

• The proposed tensor network strategy effectively handles high-connectivity lattices.
• The method simplifies complex structures, allowing for efficient simulation.
• The approach provides accurate results and shows improved performance compared to existing techniques for quantum many-body simulations.