Scaling and front dynamics in Ising quantum chains

TL;DR

This paper investigates the relaxation dynamics of an Ising quantum chain from various initial thermal states, providing explicit results for transverse magnetization evolution in different thermal configurations.

Contribution

It introduces a detailed analysis of the relaxation process in Ising chains starting from specific thermal initial states, including explicit formulas for transverse magnetization.

Findings

Explicit expressions for transverse magnetization dynamics.

Analysis of relaxation from factorized and two-temperature initial states.

Insights into thermalization processes in quantum Ising chains.

Abstract

We study the relaxation dynamics of a quantum Ising chain initially prepared in a product of canonical states corresponding each to an equilibrium state of part of the chain at a given temperature. We focus our attention on the transverse magnetization for which a general expression is given. Explicite results are given for the completely factorized initial state, corresponding to a situation where all the spins are thermalized independently, and for the two-temperatures initial state, where part of the chain called the system is thermalized at a temperature $T_s$ and the remaining part is at a temperature $T_b$.