标题： 强 disorder重正化群方法研究含长程相互作用的 bond无序反铁磁量子自旋链：基态性质 显示英文标题

标题： Strong Disorder Renormalization Group Method for Bond Disordered Antiferromagnetic Quantum Spin Chains with Long Range Interactions: Ground State Properties

摘要： 我们引入并实现了一种强 Disorder重整化群方法的空间实空间重新表述，非常适合研究键无序的反铁磁幂律耦合量子自旋链。 我们推导了配对距离分布函数的主方程$\tilde{r}$。首先，我们将其应用于短程耦合自旋链，仅保留相邻自旋之间的相互作用。我们确认其由无穷随机性不动点分布解决。然后，我们求解了所有自旋之间幂律长程相互作用的主方程，适用于从XX极限到各向异性Heisenberg极限的任意各向异性，这对应于具有长程跃迁的无序长程相互作用费米子的紧束缚链。由此我们证明了在重整化尺度$\Omega$下耦合分布函数$J$流向强 Disorder不动点分布，并且在$\tilde{r} > \rho,$处存在小修正，这些修正依赖于幂指数$\alpha$和耦合各向异性$\gamma.$。因此，低温磁化率以异常幂律发散。 单态长度 $l$ 的分布被发现以 $l^{-2}$ 的形式衰减。 对于所有 $\alpha$ 和 $\gamma$，子系统长度为 $n$ 的纠缠熵在基态下对数增长。 全局量子猝发后，纠缠熵随时间以 $S(t) \sim \ln(t)/(2\alpha)$ 的形式对数增长。 显示英文摘要

摘要： We introduce and implement a reformulation of the strong disorder renormalization group method in real space, well suited to study bond disordered antiferromagnetic power law coupled quantum spin chains. We derive the Master equations for the distribution function of pair distances $\tilde{r}$. First, we apply it to a short range coupled spin chain, keeping only interactions for adjacent spins. We confirm that it is solved by the infinite randomness fixed point distribution. Then, we solve the Master equation for the power law long range interaction between all spins for any anisotropy ranging from the XX-limit to the isotropic Heisenberg limit, corresponding to a tight binding chain of disordered long range interacting Fermions with long range hopping. We thereby show that the distribution function of couplings $J$ at renormalization scale $\Omega$ flows to the strong disorder fixed point distribution with small corrections at $\tilde{r} > \rho,$ which depend on power exponent $\alpha$ and coupling anisotropy $\gamma.$ As a consequence, the low temperature magnetic susceptibility diverges with an anomalous power law. The distribution of singlet lengths $l$ is found to decay as $l^{-2}$. The entanglement entropy of a subsystem of length $n$ increases in the ground state logarithmically for all $\alpha$ and $\gamma$. After a global quantum quench the entanglement entropy increases with time logarithmically as $S(t) \sim \ln(t)/(2\alpha)$.