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Published on: March 2, 2015
Rényi entanglement entropy of a spin chain with generative neural networks
Piotr Białas1, Piotr Korcyl2, Tomasz Stebel2
1Institute of Applied Computer Science, <a href="https://ror.org/03bqmcz70">Jagiellonian University</a>, ul. Łojasiewicza 11, 30-348 Kraków, Poland.
Abstract:
We describe a method to estimate Rényi entanglement entropy of a spin system which is based on the replica trick and generative neural networks with explicit probability estimation. It can be extended to any spin system or lattice field theory. We demonstrate our method on a one-dimensional quantum Ising spin chain. As the generative model, we use a hierarchy of autoregressive networks, allowing us to simulate up to 32 spins. We calculate the second Rényi entropy and its derivative and cross-check our results with the numerical evaluation of entropy and results available in the literature.
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