# Molecular dynamics simulation of entanglement spreading in generalized hydrodynamics

## TL;DR

This paper uses a molecular dynamics simulation method called flea gas within generalized hydrodynamics to numerically study entanglement spreading in an integrable quantum system, specifically the XXZ spin chain, after inhomogeneous quenches.

## Contribution

It applies flea gas simulations to the XXZ model for entanglement growth, providing accurate numerical results and full-time mutual information dynamics where analytical solutions are lacking.

## Key findings

- Flea gas method approximates entanglement growth well in XXZ model.
- Numerical results match analytical predictions in certain cases.
- Full-time mutual information dynamics are obtained for inhomogeneous quenches.

## Abstract

We consider a molecular dynamics method, the so-called flea gas for computing the evolution of entanglement after inhomogeneous quantum quenches in an integrable quantum system. In such systems the evolution of local observables is described at large space-time scales by the Generalized Hydrodynamics approach, which is based on the presence of stable, ballistically propagating quasiparticles. Recently it was shown that the GHD approach can be joined with the quasiparticle picture of entanglement evolution, providing results for entanglement growth after inhomogeneous quenches. Here we apply the flea gas simulation of GHD to obtain numerical results for entanglement growth. We implement the flea gas dynamics for the gapped anisotropic Heisenberg XXZ spin chain, considering quenches from globally homogeneous and piecewise homogeneous initial states. While the flea gas method applied to the XXZ chain is not exact even in the scaling limit (in contrast to the Lieb--Liniger model), it yields a very good approximation of analytical results for entanglement growth in the cases considered. Furthermore, we obtain the {\it full-time} dynamics of the mutual information after quenches from inhomogeneous settings, for which no analytical results are available.