Quenches near Ising quantum criticality as a challenge for artificial neural networks

TL;DR

This paper investigates the dynamics of quantum Ising spin chains near criticality using neural networks, comparing their effectiveness with analytical and numerical methods in capturing long-range correlations after quenches.

Contribution

It demonstrates that neural network wave function representations can accurately model complex quantum dynamics near critical points, outperforming semi-classical methods in many regimes.

Findings

Neural networks accurately reproduce long-range correlations in quantum quenches.

Semi-classical methods are effective mainly at short times and small transverse fields.

Quantitative deviations increase with system complexity and network size.

Abstract

The near-critical unitary dynamics of quantum Ising spin chains in transversal and longitudinal magnetic fields is studied using an artificial neural network representation of the wave function. A focus is set on strong spatial correlations which build up in the system following a quench into the vicinity of the quantum critical point. We compare correlations observed following reinforcement learning of the network states with analytical solutions in integrable cases and tDMRG simulations, as well as with predictions from a semi-classical discrete Truncated Wigner analysis. While the semi-classical approach excells mainly at short times and for small transverse fields, the neural-network representation provides accurate results for a much wider range of parameters. Where long-range spin-spin correlations build up in the long-time dynamics we find qualitative agreement with exact results while quantitative deviations are of similar size as for the semi-classically predicted correlations, and slow convergence is observed when increasing the number of hidden neurons.