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）的重新表述，这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，修正项取决于幂指数$\alpha$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。 单重态长度的分布被发现比之前得到的结果衰减得更慢，这对物理性质有严重的影响。 长度为$n$的子系统的纠缠熵被发现以幂律增长，而不是对数增长，对应于足够大的$\alpha$时的次体积定律。 我们认为由于彩虹态的出现，体积定律纠缠熵可能出现。 给出了一个公式$\alpha_c$，在此之下会出现这样的彩虹态。 显示英文摘要

摘要： We introduce and implement a reformulation of the strong disorder renormalization group (SDRG) 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 severe 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 for sufficiently large $\alpha$. We argue that volume law entanglement entropy can appear due to the emergence of rainbow states. A formula for $\alpha_c$ below which such rainbow states emerge is given.