Efficient Tensor Network Algorithm for Layered Systems

Area of Science:

• Condensed Matter Physics
• Quantum Many-Body Systems
• Computational Physics

Background:

• Layered 2D systems are crucial in condensed matter physics but computationally challenging to study.
• Tensor network methods have shown success in 1D and 2D systems.

Purpose of the Study:

• To develop an efficient tensor network approach for layered 2D systems.
• To capture essential interlayer correlations in these systems.
• To overcome limitations of existing numerical methods.

Main Methods:

• Developed an infinite projected entangled-pair states (iPEPS) ansatz for anisotropic 3D systems.
• Proposed a novel contraction scheme to decouple weakly interacting layers.
• Utilized 2D contraction methods for efficient computation while preserving key interlayer correlations.

Main Results:

• Benchmark results for the 3D Heisenberg model show excellent agreement with Quantum Monte Carlo and full 3D contraction.
• Successfully studied the dimer to Néel phase transition in the Shastry-Sutherland model with interlayer coupling.
• Demonstrated the method's capability for frustrated spin models intractable for Quantum Monte Carlo.

Conclusions:

• The proposed tensor network approach is efficient and accurate for layered 2D systems.
• This method extends the reach of numerical studies to complex, frustrated quantum models.
• Offers a powerful new tool for condensed matter physics research.