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The dynamical behaviour of the quantum state of different quantum spinchains, with designed site dependent interaction strengths, is analyzed whenthe initial state belongs to the one excitation subspace. It is shown that theinhomogeneous chains are able to transfer excitations with near perfectfidelity. This behaviour is found for two very different spin chainHamiltonians. The first one is the ferromagnetic Heisenberg Hamiltonian withnearest neighbor interactions, the second one describes a chain with long rangeanisotropic interactions which are ferromagnetic in the $z$ direction andantiferromagnetic in the $(x,y)$ plane. It is shown that both designed chainshave in common a partially ordered spectrum and well localized eigenvectors.This physical trait unifies the description of both kind of systems.

Understanding the propagation of excitations in quantum spin chains with different kind of interactions