标题： 键无序反铁磁量子自旋链与长程相互作用 显示英文标题

标题： Bond Disordered Antiferromagnetic Quantum Spin Chains with Long Range Interactions

摘要： 我们引入并实现了实空间中强无序重正化群（SDRG）方法的重新表述，该方法非常适合研究具有键无序幂律长程耦合的反铁磁量子自旋链。 我们推导了耦合的分布函数$J$，并对之前推导出的强无序固定点分布进行了修正，这些修正取决于幂指数$\alpha$和耦合各向异性$\gamma.$。因此，低温磁化率被发现以异常幂律发散。 单态长度的分布被发现比之前得到的衰减得更慢，这对物理性质有影响。 因此，长度为$n$的子系统的纠缠熵以幂律增长，而不是对数增长，对应于子体积定律。 虽然我们发现对于任何$\alpha$，基态都没有体积定律的纠缠熵，但我们推导出在临界值$\alpha_c\approx 1.5$以下激发态为彩虹态的概率是有限的，这导致$\alpha < 0.4$中的体积定律纠缠，其中彩虹态的形成是确定的。 显示英文摘要

摘要： We introduce and implement a reformulation of the strong disorder renormalization group (SDRG) method in real space, which is well suited to study bond disordered power law long range coupled, antiferromagnetic quantum spin chains. We derive the distribution function of couplings $J$ with corrections to the previously derived strong disorder fixed point distribution, which depend on power exponent $\alpha$ and coupling anisotropy $\gamma.$ As a consequence, the low temperature magnetic susceptibility is found to diverge with an anomalous power law. The distribution of singlet lengths is found to decay more slowly than obtained previously, with consequences for physical properties. The entanglement entropy of a subsystem of length $n$ is thereby found to increase with a power law, rather than logarithmically, corresponding to a subvolume law. While we find no volume law entanglement entropy for the ground state for any $\alpha$, we derive a finite probability that excited states are rainbow states below a critical value $\alpha_c\approx 1.5$, which leads to volume law entanglement for $\alpha < 0.4$, where the rainbow state formation is certain.