Relaxation Dynamics of Disordered Spin Chains: Localization and the Existence of a Stationary State

TL;DR

This paper investigates how disordered spin chains relax after a sudden change in their Hamiltonian, showing that the presence of a stationary state depends on spectral and localization properties rather than initial conditions.

Contribution

It provides analytical and numerical evidence that stationary states in disordered spin chains are determined by spectral and localization features of the Hamiltonian, not initial states.

Findings

Stationary state existence depends on spectral and localization properties.

Analytical and numerical methods confirm the role of Hamiltonian characteristics.

Results applicable to both integrable and nonintegrable models.

Abstract

We study the unitary relaxation dynamics of disordered spin chains following a sudden quench of the Hamiltonian. We give analytical arguments, corroborated by specific numerical examples, to show that the existence of a stationary state depends crucially on the spectral and localization properties of the final Hamiltonian, and not on the initial state. We test these ideas on integrable one-dimensional models of the Ising or XY class, but argue more generally on their validity for more complex (nonintegrable) models.