Locally quasi-stationary states in noninteracting spin chains

TL;DR

This paper defines and constructs locally quasi-stationary states in inhomogeneous noninteracting spin chains, providing a rigorous framework and explicit solutions within a generalized XY model, advancing the understanding of hydrodynamics in integrable systems.

Contribution

It formally characterizes LQSSs as an invariant subspace under dynamics and explicitly constructs these states in a generalized XY model, including a generalized hydrodynamic theory.

Findings

Identified the set of LQSSs as an invariant subspace under time evolution.

Explicit construction of LQSSs in a generalized XY model.

Developed an exact generalized hydrodynamic theory with quantum corrections.

Abstract

Locally quasi-stationary states (LQSS) were introduced as inhomogeneous generalisations of stationary states in integrable systems. Roughly speaking, LQSSs look like stationary states, but only locally. Despite their key role in hydrodynamic descriptions, an unambiguous definition of LQSSs was not given. By solving the dynamics in inhomogeneous noninteracting spin chains, we identify the set of LQSSs as a subspace that is invariant under time evolution, and we explicitly construct the latter in a generalised XY model. As a by-product, we exhibit an exact generalised hydrodynamic theory (including "quantum corrections").