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arXiv:2410.14466 · Physical Review Letters

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

Andrea Bulgarelli, Elia Cellini, Karl Jansen, Stefan Kühn, Alessandro Nada, Shinichi Nakajima, Kim A. Nicoli, Marco Panero C

Published Apr 15, 2025• 7 citations
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Abstract

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 ϕ^{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.

DOI
10.1103/physrevlett.134.151601

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The determination of entanglement measures in SU(N) gauge theories is a non-trivial task. With the so-called "replica trick", a family of entanglement measures, known as "Rényi entropies", can be determined with lattice Monte Carlo. Unfortunately, the standard implementation of the replica method for SU(N) lattice gauge theories suffers from a severe signal-to-noise ratio problem, rendering high-precision studies of Rényi entropies prohibitively expensive. In this work, we propose a method to overcome the signal-to-noise ratio problem and show some first results for SU(N) in 4 dimensions.