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Loop Optimization for Tensor Network Renormalization.

Shuo Yang1, Zheng-Cheng Gu1,2, Xiao-Gang Wen1,3

  • 1Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada.

Physical Review Letters
|April 4, 2017
PubMed
Summary
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We developed a new tensor renormalization group (TRG) scheme to simplify complex two-dimensional tensor networks. This method improves accuracy and stability for classical and quantum systems, even near critical points.

Area of Science:

  • Condensed Matter Physics
  • Quantum Information Theory
  • Computational Physics

Background:

  • Tensor networks are powerful tools for simulating quantum many-body systems.
  • Existing renormalization group (RG) methods face challenges with accuracy and stability, especially for systems off criticality.

Purpose of the Study:

  • To introduce a novel tensor renormalization group (TRG) scheme for coarse-graining 2D tensor networks.
  • To enhance the accuracy and stability of RG flow for both classical and quantum systems.

Main Methods:

  • Deforming a 2D tensor network into small loops.
  • Optimizing tensors on each loop to remove short-range entanglement iteratively.
  • Applying the scheme to classical and quantum models.

Related Experiment Videos

Main Results:

  • The proposed TRG scheme successfully coarse-grains 2D tensor networks.
  • The method demonstrates improved accuracy and stability in renormalization flow.
  • Effective application shown in the classical Ising model and a frustrated 2D quantum model.

Conclusions:

  • The new TRG scheme offers a robust approach for tensor network simulations.
  • It effectively handles entanglement and improves computational efficiency.
  • This method is applicable to a wide range of classical and quantum systems.