随机自旋链中的关联振幅和纠缠熵
Correlation amplitude and entanglement entropy in random spin chains
摘要：
利用强无序重整化群、数值精确对角化和量子蒙特卡罗方法，我们重新研究了随机反铁磁XXZ自旋1/2链的平均自旋-自旋关联函数C（l）= \upsilon l^{-η}的长长度和基态行为.除了众所周知的普适（无序无关）幂律指数η=2，我们发现有趣的普适功能显示的前因子\upsilon = \upsilon_o /3，如果l是奇数，和\upsilon = \upsilon_e /3，否则。虽然\upsilon_o和\upsilon_e是非通用的（疾病依赖性的）并且在大小上是不同的，但是如果C沿着对称（纵向）轴计算，则组合\upsilon_o + \upsilon_e = -1/4是通用的。在重整化群的框架下讨论了前因子的非普适性的起源，其中考虑了一个可解的玩具模型。此外，我们还将平均关联函数与平均纠缠熵联系起来，后者的幅度最近已被证明是普遍的。的nonuniversalities的前因子只有助于表面条款的熵。最后，我们讨论了实验相关性，我们的结果通过计算的结构因子的缩放特性，有趣的是，依赖于相关的前因子。
英文摘要：
Using strong-disorder renormalization group, numerical exact diagonalization, and quantum Monte Carlo methods, we revisit the random antiferromagnetic XXZ spin-1/2 chain focusing on the long-length and ground-state behavior of the average time-independent spin-spin correlation function C(l)=\upsilon l^{-η}. In addition to the well-known universal (disorder-independent) power-law exponent η=2, we find interesting universal features displayed by the prefactor \upsilon=\upsilon_o/3, if l is odd, and \upsilon=\upsilon_e/3, otherwise. Although \upsilon_o and \upsilon_e are nonuniversal (disorder dependent) and distinct in magnitude, the combination \upsilon_o + \upsilon_e = -1/4 is universal if C is computed along the symmetric (longitudinal) axis. The origin of the nonuniversalities of the prefactors is discussed in the renormalization-group framework where a solvable toy model is considered. Moreover, we relate the average correlation function with the average entanglement entropy, whose amplitude has been recently shown to be universal. The nonuniversalities of the prefactors are shown to contribute only to surface terms of the entropy. Finally, we discuss the experimental relevance of our results by computing the structure factor whose scaling properties, interestingly, depend on the correlation prefactors.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
