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arXiv · 2301.09469

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

E. B. Fel'dman·A. I. Zenchuk
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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.

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E. B. Fel'dman, A. I. Zenchuk. 2023-01-23. Nearest-neighbor approximation in one-excitation state evolution along spin-1/2 chain governed by XX-Hamiltonian. https://doi.org/10.1016/j.physleta.2022.128572

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