Entanglement entropy from non-equilibrium Monte Carlo simulations

Abstract

We study the entanglement entropy in lattice field theory using a simulation algorithm based on Jarzynski's theorem. We focus on the entropic c-function for the Ising model in two and in three dimensions: after validating our algorithm against known analytical results from conformal field theory in two dimensions, we present novel results for the three-dimensional case. We show that our algorithm, which is highly parallelized on graphics processing units, allows one to precisely determine the subleading corrections to the area law, which have been investigated in many recent works. Possible generalizations of this study to other strongly coupled theories are discussed.

1+33 pages; v2: typos corrected, matches published version

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• Numerical determination of the width and shape of the effective string using Stochastic Normalizing Flows
• Deep learning lattice gauge theories
• Scaling of Stochastic Normalizing Flows in $\mathrm{SU}(3)$ lattice gauge theory
• Flow-Based Sampling for Entanglement Entropy and the Machine Learning of Defects
• Rényi entanglement entropy of spin chain with Generative Neural Networks
• Resummation-based Quantum Monte Carlo for Entanglement Entropy Computation
• Universal term of Entanglement Entropy in the $\pi$-flux Hubbard model
• Scaling flow-based approaches for topology sampling in $\mathrm{SU}(3)$ gauge theory
• Casimir effect in critical $\mathrm{O}(N)$ models from non-equilibrium Monte Carlo simulations
• Hierarchical autoregressive neural networks in three-dimensional statistical system