Domain wall dynamics of the Ising chain in a transverse field

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.