Estimation of the reduced density matrix and entanglement entropies using autoregressive networks
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866914576674586624 |
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| author | Białas, Piotr Korcyl, Piotr Stebel, Tomasz Zapolski, Dawid |
| author_facet | Białas, Piotr Korcyl, Piotr Stebel, Tomasz Zapolski, Dawid |
| contents | We present an application of autoregressive neural networks to Monte Carlo simulations of quantum spin chains using the correspondence with classical two-dimensional spin systems. We use a hierarchy of neural networks capable of estimating conditional probabilities of consecutive spins to evaluate elements of reduced density matrices directly. Using the Ising chain as an example, we calculate the continuum limit of the ground state's von Neumann and Rényi bipartite entanglement entropies of an interval built of up to 5 spins. We demonstrate that our architecture is able to estimate all the needed matrix elements with just a single training for a fixed time discretization and lattice volume. Our method can be applied to other types of spin chains, possibly with defects, as well as to estimating entanglement entropies of thermal states at non-zero temperature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_04170 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Estimation of the reduced density matrix and entanglement entropies using autoregressive networks Białas, Piotr Korcyl, Piotr Stebel, Tomasz Zapolski, Dawid Quantum Physics Statistical Mechanics Machine Learning High Energy Physics - Lattice High Energy Physics - Theory We present an application of autoregressive neural networks to Monte Carlo simulations of quantum spin chains using the correspondence with classical two-dimensional spin systems. We use a hierarchy of neural networks capable of estimating conditional probabilities of consecutive spins to evaluate elements of reduced density matrices directly. Using the Ising chain as an example, we calculate the continuum limit of the ground state's von Neumann and Rényi bipartite entanglement entropies of an interval built of up to 5 spins. We demonstrate that our architecture is able to estimate all the needed matrix elements with just a single training for a fixed time discretization and lattice volume. Our method can be applied to other types of spin chains, possibly with defects, as well as to estimating entanglement entropies of thermal states at non-zero temperature. |
| title | Estimation of the reduced density matrix and entanglement entropies using autoregressive networks |
| topic | Quantum Physics Statistical Mechanics Machine Learning High Energy Physics - Lattice High Energy Physics - Theory |
| url | https://arxiv.org/abs/2506.04170 |