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arXiv:2304.13412 · Physical review. E

Mutual information of spin systems from autoregressive neural networks

P. Białas, Piotr Korcyl, Tomasz Stebel

Published Oct 24, 2023• 2 citations
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Abstract

We describe a direct method to estimate the bipartite mutual information of a classical spin system based on Monte Carlo sampling enhanced by autoregressive neural networks. It enables us to study arbitrary geometries of subsystems, and it can be generalized to classical field theories. We demonstrate it on the Ising model for four partitionings, including a multiply connected even-odd division. We show that the area law is satisfied for temperatures away from the critical temperature: the constant term is universal, whereas the proportionality coefficient is different for the even-odd partitioning.

DOI
10.1103/physreve.108.044140

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Characterizing correlations in a quantum system on the basis of the results of the projective measurements can be performed with different means including the calculation of the classical mutual information. Generally, estimating such information-entropy-based quantities requires having complete statistics of the system's states. Here we explore the possibility to reconstruct the classical mutual information and specific entropy of a quantum system with a neural network approach on the basis of a limited number of projective measurements. As a prominent example we consider the antiferromagnetic quantum Ising model in transverse and longitudinal magnetic fields which is in demand in both condensed matter physics and quantum computing. We show that the neural network approach gives reliable estimates of the classical mutual information even in the case of paramagnetic wave functions delocalized in the state space. In addition, the phase diagram of the considered quantum system is reconstructed with a special focus on discriminating various types of disordered states.
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