标题： 许多邻居少量纠缠：变范围扩展伊辛模型中的一个奇特标度 显示英文标题

标题： Many neighbors little entanglement: A curious scaling in the variable-range extended Ising model

摘要： 我们研究了在存在横向磁场的一维晶格上精确可解的变程扩展伊辛模型中，量子比特基态的两点关联函数和双部分纠缠。 我们通过改变每个量子比特的配位数$\mathcal{Z}$来引入相互作用范围的变化，其中距离为$r$的一对量子比特之间的相互作用强度按$\sim r^{-\alpha}$变化。 我们证明，关联函数的代数性质仅在$r=\mathcal{Z}$以内存在，超过该值后则表现出短程指数衰减。 我们还证明，在临界点，双部分纠缠随着配位数的增加而呈现幂律衰减（$\sim\mathcal{Z}^{-\gamma}$），无论分割大小以及$\alpha$的值如何，对于$\alpha>1$而言。 我们进一步考虑从系统无限场极限的基态开始的系统突然淬火，通过开启临界哈密顿量，并证明长时间平均的双部分纠缠表现出与$\sim\mathcal{Z}^{-\gamma}$类似的定性变化（$\mathcal{Z}$）。 显示英文摘要

摘要： We study the two-point correlation functions and the bipartite entanglement in the ground state of the exactly-solvable variable-range extended Ising model of qubits in the presence of a transverse field on a one-dimensional lattice. We introduce the variation in the range of interaction by varying the coordination number, $\mathcal{Z}$, of each qubit, where the interaction strength between a pair of qubits at a distance $r$ varies as $\sim r^{-\alpha}$. We show that the algebraic nature of the correlation functions is present only up to $r=\mathcal{Z}$, above which it exhibits short-range exponential scaling. We also show that at the critical point, the bipartite entanglement exhibits a power-law decrease ($\sim\mathcal{Z}^{-\gamma}$) with increasing coordination number irrespective of the partition size and the value of $\alpha$ for $\alpha>1$. We further consider a sudden quench of the system starting from the ground state of the infinite-field limit of the system Hamiltonian via turning on the critical Hamiltonian, and demonstrate that the long-time averaged bipartite entanglement exhibits a qualitatively similar variation ($\sim\mathcal{Z}^{-\gamma}$) with $\mathcal{Z}$.