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Domain wall dynamics of the Ising chains in a transverse field

V. Subrahmanyam
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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.

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V. Subrahmanyam. 2003-08-20. Domain wall dynamics of the Ising chains in a transverse field. https://doi.org/10.1103/physrevb.68.212407

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