XX-哈密顿量控制下自旋1/2链单激发态演化的最近邻近似
Nearest-neighbor approximation in one-excitation state evolution along spin-1/2 chain governed by XX-Hamiltonian
摘要：
当自旋-自旋相互作用的强度为$\sim 1/r^3$时，最近邻相互作用（NNI）近似被广泛用于具有偶极-偶极相互作用（DDI）的短时自旋动力学，其中$r$是这些自旋之间的距离。然而，NNI不能近似这类系统的长时间演化。我们考虑了自旋-自旋相互作用强度为$\sim 1/r^α$，$α\ge 3$的系统，并找到了NNI对由$XX$ -Hamilton控制的均匀自旋链中任意单激发初量子态演化的适用性的下界$α_c$.我们得到了$α_c$对链长的对数依赖性。
英文摘要：
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 $\sim 1/r^α$, $α\ge 3$, and find the low boundary $α_c$ 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 $α_c$ on the chain length.
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