Neural Networks as Universal Probes of Many-Body Localization in Quantum Graphs

TL;DR

This paper demonstrates that neural networks trained on entanglement spectra can generalize to identify ergodic and localized phases in various quantum systems, offering a new computational approach for many-body physics.

Contribution

The study introduces a neural network trained on a specific quantum model that can accurately predict phase transitions and mobility edges in different models without retraining.

Findings

Neural network accurately predicts phase boundaries in extended models.

Model generalizes well to different graph topologies.

Machine learning offers a new tool for exploring many-body localization.

Abstract

We show that a neural network, trained on the entanglement spectra of a nearest neighbor Heisenberg chain in a random transverse magnetic field, can be used to efficiently study the ergodic/many-body localized properties of a number of other quantum systems, without further re-training. We benchmark our computational architecture against a $J_{1}\!\!-\!\!J_{2}$ - model, which extends the Heisenberg chain to include next-to-nearest neighbor interactions, with excellent agreement with known results. When applied to Hamiltonians that differ from the training model by the topology of the underlying graph, the neural network is able to predict the critical disorders and, more generally, shapes of the mobility edge that agree with our heuristic expectation. We take this as proof of principle that machine learning algorithms furnish a powerful new set of computational tools to explore the many-body physics frontier.