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Truncating loopy tensor networks by zero-mode gauge fixing.

Ihor Sokolov1,2, Yintai Zhang1,3, Jacek Dziarmaga1,2

  • 1Jagiellonian University, Institute of Theoretical Physics, Faculty of Physics, Astronomy and Applied Computer Science, ul. Łojasiewicza 11, 30-348 Kraków, Poland.

Physical Review. E
|December 23, 2025
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Summary
This summary is machine-generated.

Loopy tensor networks are compressed inefficiently due to internal correlations. This study introduces a local bond optimization method that improves compression by utilizing loop correlations for better truncation, outperforming standard initialization.

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Area of Science:

  • Condensed matter physics
  • Quantum information theory
  • Numerical methods in physics

Background:

  • Loopy tensor networks, such as infinite projected entangled-pair states (iPEPS) and periodic matrix product states (pMPS), exhibit complex internal correlations.
  • These correlations often lead to inefficiencies in standard compression techniques, hindering accurate numerical simulations.

Purpose of the Study:

  • To develop an improved compression method for loopy tensor networks.
  • To enhance the efficiency and accuracy of tensor network algorithms by optimizing bond dimensions.

Main Methods:

  • A novel local bond optimization technique is proposed that leverages local loop correlations.
  • The method involves cutting bonds to define states, utilizing their linear dependence for truncation.
  • Linear dependence is resolved using zero modes of the states' metric tensor.

Main Results:

  • The proposed method demonstrates improved initial truncation errors compared to standard initialization techniques.
  • Successful application to infinite projected entangled-pair states (iPEPS) and periodic matrix product states (pMPS) within the tensor renormalization group (TRG) context.
  • Validation through various illustrative examples showcasing superior performance.

Conclusions:

  • Local bond optimization offers a more effective approach to compressing loopy tensor networks.
  • The method provides a significant improvement in initial truncation accuracy for tensor network states.
  • This technique enhances the efficiency of numerical simulations involving complex quantum systems.