S=1/2 magnetic chains as domain wall systems

Abstract

The authors describe S=1/2 Ising-like magnetic chains completely in terms of domain walls. They formulate domain wall creation and annihilation operators as fermion operators and calculate the domain wall content of the ground state and of excited states. From exact results for finite chains and from the solution in the one-domain wall subspace they find that a single domain wall behaves like a free particle in a well. The transition between the two equivalent ground states of Ising-like S=1/2 chains is found to be dominated by quantum diffusion: the approach of the magnetization to the asymptotic behaviour is algebraic and not exponential. The analogy of this observation to interface fluctuations in the two-dimensional classical system is pointed out. For domain walls in the presence of impurities they study the phase shift and the transmission coefficient as well as the exact energy spectrum of finite impure lattices. To visualize the domain wall scattering they also demonstrate their real-time dynamics.