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The approximation of nearest neighbor interaction (NNI) is widely used inshort-time spin dynamics with dipole-dipole interactions (DDI) when theintensity of spin-spin interaction is $\sim 1/r^3$, where $r$ is a distancebetween those spins. However, NNI can not approximate the long time evolutionin such systems. We consider the system with the intensity of the spin-spininteraction $\sim 1/r^{\alpha}$, $\alpha\ge 3$, and find the low boundary$\alpha_c$ of applicability of the NNI to the evolution of an arbitraryone-excitation initial quantum state in the homogeneous spin chain governed bythe $XX$-Hamiltonian. We obtain the logarithmic dependence of $\alpha_c$ on thechain length.

Nearest-neighbor approximation in one-excitation state evolution along spin-1/2 chain governed by XX-Hamiltonian