Machine Learning Many-Body Localization: Search for the Elusive Nonergodic Metal

TL;DR

This paper uses neural networks to investigate the existence of a nonergodic metallic phase in a quantum system with a quasiperiodic potential, providing a new machine learning approach to phase detection.

Contribution

It introduces a neural-network-based method to identify nonergodic metallic phases using many-body entanglement spectra, advancing phase detection techniques in quantum systems.

Findings

Identifies a nonergodic metallic phase at intermediate potential strength

Demonstrates neural networks can locate phase boundaries accurately

Provides evidence for the existence of a nonergodic metallic phase

Abstract

The breaking of ergodicity in isolated quantum systems with a single-particle mobility edge is an intriguing subject that has not yet been fully understood. In particular, whether a nonergodic but metallic phase exists or not in the presence of a one-dimensional quasiperiodic potential is currently under active debate. In this Letter, we develop a neural-network-based approach to investigate the existence of this nonergodic metallic phase in a prototype model using many-body entanglement spectra as the sole diagnostic. We find that such a method identifies with high confidence the existence of a nonergodic metallic phase in the midspectrum at an intermediate quasiperiodic potential strength. Our neural-network based approach shows how supervised machine learning can be applied not only in locating phase boundaries but also in providing a way to definitively examine the existence or not of a novel phase.