Toward the Thermodynamic Limit: Neural Operators for Non-equilibrium Dynamics of Mott Insulators

TL;DR

This paper demonstrates that Fourier Neural Operators can learn to predict the non-equilibrium dynamics of Mott insulators in the thermodynamic limit, enabling large-scale simulations beyond traditional computational capabilities.

Contribution

The study introduces the use of Fourier Neural Operators to accurately predict large-scale non-equilibrium dynamics of Mott insulators from small system training data.

Findings

Model predicts 1024x1024 lattice behavior in seconds

Neural operators generalize zero-shot to larger systems

Predictions match theoretical expectations for key observables

Abstract

Mott insulators exhibit complex photoexcitation dynamics under intense optical driving, with potential implications for carrier multiplication beyond the Shockley-Queisser limit. Probing these nonequilibrium processes requires access to the thermodynamic limit, where the number of lattice sites becomes arbitrarily large, but conventional solvers are constrained to small systems due to the exponential growth of the Hilbert space. Fourier Neural Operators (FNOs), originally developed for solving partial differential equations, naturally accommodate inputs of varying resolution and are capable of capturing nonlocal effects. Here, we employ FNOs to learn the mapping from noise-perturbed ground-state momentum distributions to their post-pulse counterparts across a range of interaction strengths and driving parameters. Trained only on small lattices, the model generalizes zero-shot to much larger systems, producing physically reasonable momentum distributions well beyond the reach of numerical solvers. Specifically, the model can predict momentum distribution for a 1024x1024 system within a few seconds that matches the theoretical behavior of key observables, whereas direct numerical simulations have so far been restricted to edge sizes of ~30. These results demonstrate the potential of neural operators to directly access large-scale nonequilibrium dynamics, providing a new pathway toward the thermodynamic limit in strongly correlated materials.