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Flow-Based Sampling for Entanglement Entropy and the Machine Learning of Defects
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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.
Forward citations
Cited by 7 Pith papers
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Determination of thermodynamics from entanglement entropy in the finite-density O(N) model
The derivative of entanglement entropy with respect to subregion volume equals the thermal entropy density in the large-subregion limit, verified via lattice simulations of the finite-density O(4) model using dual wor...
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Scalable Generative Sampling and Multilevel Estimation for Lattice Field Theories Near Criticality
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Scaling flow-based approaches for topology sampling in $\mathrm{SU}(3)$ gauge theory
Out-of-equilibrium simulations with open-to-periodic boundary switching plus a tailored stochastic normalizing flow enable efficient topology sampling in the continuum limit of four-dimensional SU(3) Yang-Mills theory.
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The derivative of entanglement entropy with respect to region size equals the thermal entropy density, and a generalized Maxwell relation connects it to charge density — tested nonperturbatively in the 3D O(4) model.
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Flow-based samplers numerically confirm the next-to-leading-order width and the resummed string-tension conjecture for the Nambu-Goto effective string in 2+1 dimensions.
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