Relaxation in the XX quantum chain

TL;DR

This paper analytically investigates the magnetisation relaxation dynamics of an XX quantum chain in a transverse magnetic field, considering various initial thermal states and regimes influenced by magnetic field strength and temperature.

Contribution

It provides new analytical results on the relaxation behavior of the XX quantum chain starting from thermal kink-like and droplet-like initial states.

Findings

Different relaxation regimes depending on magnetic field and temperature.

Analytical expressions for the Green function of transverse magnetisation.

Behavior of magnetisation in finite cold subsystems in contact with infinite temperature environments.

Abstract

We present the results obtained on the magnetisation relaxation properties of an XX quantum chain in a transverse magnetic field. We first consider an initial thermal kink-like state where half of the chain is initially thermalized at a very high temperature $T_b$ while the remaining half, called the system, is put at a lower temperature $T_s$. From this initial state, we derive analytically the Green function associated to the dynamical behaviour of the transverse magnetisation. Depending on the strength of the magnetic field and on the temperature of the system, different regimes are obtained for the magnetic relaxation. In particular, with an initial droplet-like state, that is a cold subsystem of finite size in contact at both ends with an infinite temperature environnement, we derive analytically the behaviour of the time-dependent system magnetisation.