Flow-Based Sampling for Entanglement Entropy and the Machine Learning of Defects

We introduce a novel technique to numerically calculate Rényi entanglement entropies in lattice quantum field theory using generative models. We describe how flow-based approaches can be combined with the replica trick using a custom neural-network architecture around a lattice defect connecting two replicas. Numerical tests for the $\phi^4$ scalar field theory in two and three dimensions demonstrate that our technique outperforms state-of-the-art Monte Carlo calculations, and exhibit a promising scaling with the defect size.

@article{bulgarelli2025_2410.14466,
  title={ Flow-Based Sampling for Entanglement Entropy and the Machine Learning of Defects },
  author={ Andrea Bulgarelli and Elia Cellini and Karl Jansen and Stefan Kühn and Alessandro Nada and Shinichi Nakajima and Kim A. Nicoli and Marco Panero },
  journal={arXiv preprint arXiv:2410.14466},
  year={ 2025 }
}