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

2024-10-18

Physical Review Letters

AI Summary

This work addresses the challenge of efficiently computing Rényi entanglement entropy in lattice quantum field theory, particularly in the presence of local defects. We propose a novel method integrating the replica trick with reversible flow-based generative models: specifically, we design the first conditional flow network architecture capable of jointly sampling multi-replica partition function ratios for coupled lattice defect configurations—yielding unbiased, high-dimensional sampling. Our approach circumvents critical slowing-down inherent to conventional Markov chain Monte Carlo methods in strongly correlated regimes. Benchmarking on 2D and 3D φ⁴ scalar field models demonstrates substantial gains in both computational efficiency and accuracy: entanglement entropy errors are reduced by an order of magnitude, and the method exhibits favorable scalability with defect size. This framework provides a broadly applicable computational paradigm for investigating how topological defects, impurities, or boundaries influence quantum entanglement in lattice field theories.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Social Networks and Social Media: Computational social science

Abstract

We introduce a novel technique to numerically calculate R'enyi 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.

Problem

• Calculate Rényi entanglement entropies in lattice QFT
• Combine flow-based sampling with replica trick
• Improve accuracy and scaling over Monte Carlo methods

Innovation

• Flow-based generative models for entanglement entropy
• Neural-network architecture with replica trick
• Outperforms Monte Carlo in scalar field theory