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

• URL: http://arxiv.org/abs/2301.09469v1
• Date: Mon, 23 Jan 2023 15:01:12 GMT
• Title: Nearest-neighbor approximation in one-excitation state evolution along spin-1/2 chain governed by XX-Hamiltonian
• Authors: E.B.Fel'dman and A.I.Zenchuk
• Abstract summary: approximation of nearest neighbor interaction (NNI) is widely used in short-time spin dynamics with dipole-dipole interactions (DDI) We consider the system with the intensity of the spin-spin interaction $sim 1/ralpha$, $alphage 3$, 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.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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