LCN

Lattice Convolutional Networks for Learning Ground States of Quantum Many-Body Systems

This is the official implementation of the LCN method proposed in the following paper.

Cong Fu*, Xuan Zhang*, Huixin Zhang, Hongyi Ling, Shenglong Xu, Shuiwang Ji. "Lattice Convolutional Networks for Learning Ground States of Quantum Many-Body Systems", SIAM International Conference on Data Mining (SDM) 2024.

Requirements

We include key dependencies below. The versions we used are in the parentheses. Our detailed environmental setup is available in quantum_env.yaml.

• PyTorch (1.9.0)
• PyTorch Geometric (1.7.2)

Preparing Data

• We use the same four kinds of lattices adopted in Kochkov et al., 2021, including square, triangular, honeycomb, and kagome.
• We put all the lattice data in the dataset folder.

Run

Example

• Train LCN on 6 $\times$ 6 triangular lattice and J2 in the Heisenberg model equals to 0:

cd scripts
bash train_triangular_N_36_J_0.sh

• Train LCN on 36 nodes kagome lattice and J2 in the Heisenberg model equals to -0.02:

cd scripts
bash train_kagome_N_36_J_-002.sh

Citation

@article{fu2022lattice,
  title={Lattice convolutional networks for learning ground states of quantum many-body systems},
  author={Fu, Cong and Zhang, Xuan and Zhang, Huixin and Ling, Hongyi and Xu, Shenglong and Ji, Shuiwang},
  journal={arXiv preprint arXiv:2206.07370},
  year={2022}
}

Acknowledgments

This work was supported in part by National Science Foundation grant IIS-1908198 and National Institutes of Health grant U01AG070112.