# Generalized hydrodynamics, quasiparticle diffusion, and anomalous local relaxation in random integrable spin chains

## TL;DR

This paper develops a generalized hydrodynamic framework for random integrable spin chains, revealing diffusive quasiparticle spreading and phase transitions between delocalized and quasi-localized states with distinct relaxation behaviors.

## Contribution

It introduces a hydrodynamic theory incorporating disorder-induced diffusion in random integrable systems, highlighting novel phase transition phenomena and anomalous relaxation.

## Key findings

- Diffusive broadening of operator fronts in random integrable systems.
- Existence of a phase transition between delocalized and quasi-localized phases.
- Anomalous power-law decay of autocorrelation functions in the localized phase.

## Abstract

We study the nonequilibrium dynamics of random spin chains that remain integrable (i.e., solvable via Bethe ansatz): because of correlations in the disorder, these systems escape localization and feature ballistically spreading quasiparticles. We derive a generalized hydrodynamic theory for dynamics in such random integrable systems, including diffusive corrections due to disorder, and use it to study non-equilibrium energy and spin transport. We show that diffusive corrections to the ballistic propagation of quasiparticles can arise even in noninteracting settings, in sharp contrast with clean integrable systems. This implies that operator fronts broaden diffusively in random integrable systems. By tuning parameters in the disorder distribution, one can drive this model through an unusual phase transition, between a phase where all wavefunctions are delocalized and a phase in which low-energy wavefunctions are quasi-localized (in a sense we specify). Both phases have ballistic transport; however, in the quasi-localized phase, local autocorrelation functions decay with an anomalous power law, and the density of states diverges at low energy.