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 $\sim 1/r^3$, 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 $\sim 1/r^{\alpha }$, $\alpha \ge 3$, and find the low boundary ${\alpha }_c$ 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 ${\alpha }_c$ on the chain length.

12 pages, 6 figures

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Cited by in corpus (1)

• One-excitation spin dynamics in homogeneous closed chain governed by XX-Hamiltonian