Domain wall dynamics of the Ising chains in a transverse field

TL;DR

This paper analyzes the dynamics of Ising spin chains in a transverse field, revealing conserved domain numbers and providing analytical solutions for magnetization and correlation functions based on initial domain configurations.

Contribution

It introduces a method to determine eigenfunctions and dynamics of the Ising chain with domain conservation, offering explicit analytical results for various initial states.

Findings

Domain number is conserved at discrete times.

Analytical expressions for local magnetization and correlation functions.

Domain size distribution expressed via Bessel functions.

Abstract

We show that the dynamics of an Ising spin chain in a transverse field conserves the number of domains (strings of down spins in an up-spin background) at discrete times. This enables the determination of the eigenfunctions of the time-evolution operator, and the dynamics of initial states with domains. The transverse magnetization is shown to be identically zero in all sectors with a fixed number of domains. For an initial state with a single string of down spins, the local magnetization, the equal-time and double-time spin-spin correlation functions, are calculated analytically as functions of time and the initial string size. The domain size distribution function can be expressed as a simple integral involving Bessel functions.