Extracting electronic many-body correlations from local measurements with artificial neural networks

The characterization of many-body correlations provides a powerful tool for analyzing correlated quantum materials. However, experimental extraction of quantum entangle-ment in correlated electronic systems remains an open problem in practice. In particu-lar, the correlation entropy quantifies the strength of quantum correlations in interact-ing electronic systems, yet it requires measuring all the single-particle correlators of a macroscopic sample. To circumvent this bottleneck, we introduce a strategy to obtain the correlation entropy of electronic systems solely from a set of local measurements. We show that, by combining local particle-particle and density-density correlations with a neural-network algorithm, the correlation entropy can be predicted accurately. Specifi-cally, we show that for a generalized interacting fermionic model, our algorithm yields an accurate prediction of the correlation entropy from a set of noisy local correlators. Our work shows that the correlation entropy in interacting electron systems can be recon-structed from local measurements, providing a starting point to experimentally extract many-body correlations with local probes.Peer reviewe