This repository provides a minimal working example of the QR-CTMRG (Corner Transfer Matrix Renormalization Group with QR decomposition) algorithm, as described in our paper:

Accelerating two-dimensional tensor network contractions using QR-decompositions Yining Zhang, Qi Yang, Philippe Corboz, 2025, (Co-first author)

Efficient iPEPS Simulation on the Honeycomb Lattice via QR-based CTMRG Qi Yang, Philippe Corboz, 2025

This code demonstrates a simple and clean implementation of the QR-CTMRG algorithm for 2D tensor network contraction, suitable for variational optimization of PEPS (Projected Entangled Pair States) and related models.

• Minimal: The code is kept as simple as possible for clarity and educational purposes.
• Heisenberg Model Example: Includes a variational optimization of the 2D Heisenberg model energy. ⚡️Extremely Fast!
• Kitaev Model Example: Includes a variational optimization of the Pure Isotropic Kitaev model energy. ⚡️Extremely Fast!

Simply run:

python heisenberg.py

• The script will perform variational optimization of a PEPS ansatz for the 2D Heisenberg model.
• Energy and timing curves will be saved as energy.png and time.png.
• All main algorithmic steps are contained in a single file for clarity.

You can adjust parameters such as chi, D, maxiter, etc. in the main() function.

If you use this code or find it helpful, please cite:

@misc{zhang2025acceleratingtwodimensionaltensornetwork,
      title={Accelerating two-dimensional tensor network contractions using QR-decompositions}, 
      author={Yining Zhang and Qi Yang and Philippe Corboz},
      year={2025},
      eprint={2505.00494},
      archivePrefix={arXiv},
      primaryClass={cond-mat.str-el},
      url={https://arxiv.org/abs/2505.00494}, 
}
@misc{yang2025efficientipepssimulationhoneycomb,
      title={Efficient iPEPS Simulation on the Honeycomb Lattice via QR-based CTMRG}, 
      author={Qi Yang and Philippe Corboz},
      year={2025},
      eprint={2509.05090},
      archivePrefix={arXiv},
      primaryClass={cond-mat.str-el},
      url={https://arxiv.org/abs/2509.05090}, 
}

• The current implementation is intentionally not the most minimal possible, especially in the basis construction part, to avoid logical errors and maintain clarity.
• For further simplification or adaptation to other models, feel free to modify the code.