Distinguishing an Anderson Insulator from a Many-Body Localized phase through space-time snapshots with Neural Networks

TL;DR

This paper introduces a machine learning approach using 3D CNNs to distinguish Anderson insulators from MBL phases based on space-time snapshots, achieving high accuracy and revealing key differences in quantum correlation propagation.

Contribution

The work demonstrates that space-time snapshot data combined with CNNs can effectively differentiate Anderson and MBL phases, highlighting the importance of temporal information in phase classification.

Findings

CNNs achieve ~80% accuracy in classifying phases.

Temporal data is crucial for accurate phase distinction.

Slower quantum correlation propagation explains classification difficulties.

Abstract

Distinguishing the dynamics of an Anderson insulator from a Many-Body Localized (MBL) phase is an experimentally challenging task. In this work, we propose a method based on machine learning techniques to analyze experimental snapshot data to separate the two phases. We show how to train $3D$ convolutional neural networks (CNNs) using space-time Fock-state snapshots, allowing us to obtain dynamic information about the system. We benchmark our method on a paradigmatic model showing MBL ($t-V$ model with quenched disorder), where we obtain a classification accuracy of $\approx 80 \%$ between an Anderson insulator and an MBL phase. We underline the importance of providing temporal information to the CNNs and we show that CNNs learn the crucial difference between an Anderson localized and an MBL phase, namely the difference in the propagation of quantum correlations. Particularly, we show that the misclassified MBL samples are characterized by an unusually slow propagation of quantum correlations, and thus the CNNs label them wrongly as Anderson localized. Finally, we apply our method to the case with quasi-periodic potential, known as the Aubry-Andr\'e model (AA model). We find that the CNNs have more difficulties in separating the two phases. We show that these difficulties are due to the fact that the MBL phase of the AA model is characterized by a slower information propagation for numerically accessible system sizes.