Off equilibrium dynamics in disordered quantum spin chain

TL;DR

This paper investigates the non-equilibrium dynamics of a disordered quantum spin chain, revealing algebraic decay and correlation buildup, supported by numerical and analytical methods.

Contribution

It provides new insights into the time evolution of disordered quantum chains, combining numerical simulations with analytical reasoning.

Findings

Algebraic decay of magnetisation and correlations over time

Correlation functions reach size-dependent stationary values

Analytical support for numerical observations

Abstract

We study the non-equilibrium time evolution of the average transverse magnetisation and end-to-end correlation functions of the random Ising quantum chain. Starting with fully magnetised states, either in the $x$ or $z$ direction, we compute numerically the average quantities. They show similar behaviour to the homogeneous chain, that is an algebraic decay in time toward a stationary state. During the time evolution, the spatial correlations, measured from one end to the other of the chain, are building up and finally at long time they reach a size-dependent constant depending on the distance from criticality. Analytical arguments are given which support the numerical results.