Discovering hydrodynamic equations of many-body quantum systems

TL;DR

This paper introduces a machine learning framework that automatically discovers hydrodynamic equations for quantum many-body systems from limited data, simplifying the analysis of complex quantum dynamics and unveiling new effective descriptions.

Contribution

The authors develop a novel machine learning approach to derive hydrodynamic equations directly from data, bypassing complex analytical derivations and enabling discovery of new equations in quantum systems.

Findings

Reproduced known hydrodynamic equations for integrable models

Discovered novel hydrodynamic equations for interacting systems

Provided interpretable models for quantum material properties

Abstract

Simulating and predicting dynamics of quantum many-body systems is extremely challenging, even for state-of-the-art computational methods, due to the spread of entanglement across the system. However, in the long-wavelength limit, quantum systems often admit a simplified description, which involves a small set of physical observables and requires only a few parameters such as sound velocity or viscosity. Unveiling the relationship between these hydrodynamic equations and the underlying microscopic theory usually requires a great effort by condensed matter theorists. In the present paper, we develop a new machine-learning framework for automated discovery of effective equations from a limited set of available data, thus bypassing complicated analytical derivations. The data can be generated from numerical simulations or come from experimental quantum simulator platforms. Using integrable models, where direct comparisons can be made, we reproduce previously known hydrodynamic equations, strikingly discover novel equations and provide their derivation whenever possible. We discover new hydrodynamic equations describing dynamics of interacting systems, for which the derivation remains an outstanding challenge. Our approach provides a new interpretable method to study properties of quantum materials and quantum simulators in non-perturbative regimes.