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

Abstract

The approximation of nearest neighbor interaction (NNI) is widely used in short-time spin dynamics with dipole-dipole interactions (DDI) when the intensity of spin-spin interaction is ∼1/r3, where r is a distance between those spins. However, NNI can not approximate the long time evolution in such systems. We consider the system with the intensity of the spin-spin interaction ∼1/rα, α≥3, and find the low boundary αc of applicability of the NNI to the evolution of an arbitrary one-excitation initial quantum state in the homogeneous spin chain governed by the XX-Hamiltonian. We obtain the logarithmic dependence of αc on the chain length.