# Transport in out-of-equilibrium XXZ chains: non-ballistic behavior and correlation functions

## TL;DR

This paper investigates non-ballistic spin transport in out-of-equilibrium XXZ chains, revealing abrupt magnetization jumps linked to local conservation laws, with theoretical predictions confirmed by tDMRG simulations.

## Contribution

It introduces a novel explanation for abrupt magnetization jumps in XXZ chains using generalized hydrodynamics and conservation laws, supported by numerical simulations.

## Key findings

- Magnetization profiles can exhibit abrupt jumps not predicted by standard hydrodynamics.
- Jumps propagate at velocities of the heaviest quasiparticles.
- The theory accurately describes long-time steady profiles of charges and correlations.

## Abstract

We consider the nonequilibrium protocol where two semi-infinite gapped XXZ chains, initially prepared in different equilibrium states, are suddenly joint together. At large times, a generalized hydrodynamic description applies, according to which the system can locally be represented by space- and time- dependent stationary states. The magnetization displays an unusual behavior: depending on the initial state, its profile may exhibit abrupt jumps that can not be predicted directly from the standard hydrodynamic equations and which signal non-ballistic spin transport. We ascribe this phenomenon to the structure of the local conservation laws and make a prediction for the exact location of the jumps. We find that the jumps propagate at the velocities of the heaviest quasiparticles. By means of tDMRG simulations we show that our theory yields a complete description of the long-time steady profiles of conserved charges, currents, and local correlations.