Autoregressive Neural Network Extrapolation of Quantum Spin Dynamics Across Time and Space

TL;DR

This paper presents an autoregressive machine learning method trained on tensor network simulations to accurately extrapolate long-time and large-scale quantum spin dynamics, surpassing traditional computational limits.

Contribution

It introduces a novel autoregressive neural network framework that extends quantum spin dynamics beyond conventional numerical methods, demonstrating robustness and superior performance.

Findings

Outperforms convolutional neural networks and linear regression in long-time extrapolation.

Exhibits high robustness to perturbations in predictions.

Successfully extrapolates dynamics in gapless quantum systems beyond existing methods.

Abstract

Understanding the dynamical response of quantum materials is central to revealing their microscopic properties, yet access to long-time and large-scale dynamics remains severely limited by rapidly growing computational costs and entanglement, particularly in gapless systems. Here we introduce an autoregressive machine-learning framework that enables the extrapolation of dynamical spin correlations in both time and space beyond the reach of conventional numerical methods. Trained on time-dependent density matrix renormalization group simulations of the gapless XXZ model, our approach is benchmarked against exact solutions available for this analytically solvable system. Combined with physics-informed spatial extension, multi-layer perceptron model using ReLU activation functions has been shown to be superior than convolutional neural networks and linear regressions for longer time extrapolation. Perturbation study of error accumulation further demonstrates that our autoregressive neural network extrapolations are highly robust to perturbations, suggesting stable and reliable predictions. This work establishes a new paradigm for studying the dynamics of gapless quantum many-body systems, in which machine learning extends and complements the capabilities of state-of-the-art numerical approaches.