无序量子线结的纠缠熵
Entanglement Entropy of Disordered Quantum Wire Junctions
摘要：
我们考虑了不同的无序晶格模型组成的$M$线性链粘在一起的星形方式，并研究了一个臂和系统的其余部分之间的纠缠标度使用数值强无序重整化群方法。对于所研究的所有模型，随机横场伊辛模型（RTIM），随机XX自旋模型，并与随机最近邻跳跃项的自由费米子模型，平均纠缠熵被发现增加的长度$L$的臂根据$S(L)=\frac{c_{\rm eff}}{6}\ln L+const$的形式。对于RTIM和XX模型，有效中心荷$c_{\rm eff}$在结的细节上是通用的，并且只取决于$M$的臂数.有趣的是，对于RTIM，$c_{\rm eff}$随$M$降低，而对于XX模型，它增加。对于自由费米子模型，$c_{\rm eff}$还依赖于结的细节，这与模型的亚晶格对称性有关。在这种情况下，可以通过适当的结几何形状实现$M$的增加和减少趋势。
英文摘要：
We consider different disordered lattice models composed of $M$ linear chains glued together in a star-like manner, and study the scaling of the entanglement between one arm and the rest of the system using a numerical strong-disorder renormalization group method. For all studied models, the random transverse-field Ising model (RTIM), the random XX spin model, and the free-fermion model with random nearest-neighbor hopping terms, the average entanglement entropy is found to increase with the length $L$ of the arms according to the form $S(L)=\frac{c_{\rm eff}}{6}\ln L+const$. For the RTIM and the XX model, the effective central charge $c_{\rm eff}$ is universal with respect to the details of junction, and only depends on the number $M$ of arms. Interestingly, for the RTIM $c_{\rm eff}$ decreases with $M$, whereas for the XX model it increases. For the free-fermion model, $c_{\rm eff}$ depends also on the details of the junction, which is related to the sublattice symmetry of the model. In this case, both increasing and decreasing tendency with $M$ can be realized with appropriate junction geometries.
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