# Emergent hydrodynamics in non-equilibrium quantum systems

## TL;DR

This paper introduces a numerical method called density matrix truncation (DMT) to study the late-time dynamics of large-scale Floquet and static quantum systems, revealing insights into prethermalization, heating, and hydrodynamics.

## Contribution

The paper demonstrates that DMT accurately captures Floquet physics and emergent hydrodynamics in large quantum systems, providing a new tool for analyzing non-equilibrium quantum dynamics.

## Key findings

- DMT captures prethermalization and heating in Floquet systems.
- Interplay between Floquet heating and transport affects system dynamics.
- DMT enables extraction of energy diffusion coefficients in large spin chains.

## Abstract

A tremendous amount of recent attention has focused on characterizing the dynamical properties of periodically driven many-body systems. Here, we use a novel numerical tool termed `density matrix truncation' (DMT) to investigate the late-time dynamics of large-scale Floquet systems. We find that DMT accurately captures two essential pieces of Floquet physics, namely, prethermalization and late-time heating to infinite temperature. Moreover, by implementing a spatially inhomogeneous drive, we demonstrate that an interplay between Floquet heating and diffusive transport is crucial to understanding the system's dynamics. Finally, we show that DMT also provides a powerful method for quantitatively capturing the emergence of hydrodynamics in static (un-driven) Hamiltonians; in particular, by simulating the dynamics of generic, large-scale quantum spin chains (up to L = 100), we are able to directly extract the energy diffusion coefficient.