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

TL;DR

This paper presents a neural network-based method to estimate the quantum correlation entropy of electronic systems using only local measurements, bypassing the need for full correlator data.

Contribution

It introduces a novel approach combining local measurements with neural networks to accurately predict many-body correlation entropy in electronic systems.

Findings

Neural network accurately predicts correlation entropy from local correlators.

Method works reliably even with noisy local measurement data.

Enables experimental extraction of many-body correlations from local probes.

Abstract

The characterization of many-body correlations provides a powerful tool for analyzing correlated quantum materials. However, experimental extraction of quantum entanglement in correlated electronic systems remains an open problem in practice. In particular, the correlation entropy quantifies the strength of quantum correlations in interacting 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 demonstrate that by combining local particle-particle and density-density correlations with a neural-network algorithm, the correlation entropy can be predicted accurately. Specifically, 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 demonstrates that the correlation entropy in interacting electron systems can be reconstructed from local measurements, providing a starting point to experimentally extract many-body correlations with local probes.