# Magnetization and entanglement after a geometric quench in the XXZ chain

## TL;DR

This paper studies the non-equilibrium dynamics of the XXZ spin chain after a geometric quench, analyzing magnetization, entanglement, and fluctuations using numerical and theoretical methods.

## Contribution

It provides a detailed numerical and analytical study of magnetization and entanglement dynamics post-quench, including a new ansatz for the noninteracting case and comparison with generalized hydrodynamics.

## Key findings

- Magnetization profiles agree well with generalized hydrodynamics predictions.
- Entanglement entropy propagation is characterized and an ansatz for the XX case is proposed.
- Magnetization fluctuations are proportional to entanglement entropy at leading order.

## Abstract

We investigate the dynamics of the XXZ spin chain after a geometric quench, which is realized by connecting two half-chains prepared in their ground states with zero and maximum magnetizations, respectively. The profiles of magnetization after the subsequent time evolution are studied numerically by density-matrix renormalization group methods, and a comparison to the predictions of generalized hydrodynamics yields a very good agreement. We also calculate the profiles of entanglement entropy and propose an ansatz for the noninteracting XX case, based on arguments from conformal field theory. In the general interacting case, the propagation of the entropy front is studied numerically both before and after the reflection from the chain boundaries. Finally, our results for the magnetization fluctuations indicate a leading order proportionality relation to the entanglement entropy.