论文标题
通过本地化范围的转变和不均匀调制的纠缠缩放
Entanglement scaling in fermion chains with a localization-delocalization transition and inhomogeneous modulations
论文作者
论文摘要
我们通过数值计算其最近确定的上限和上限，研究了临界费链中相邻子系统之间的对数负相位的缩放。对于随机耦合以及对耦合的相关的大道调制，该耦合诱导了一个上的单重状态，因此发现边界与子系统大小相对增加，并且两个先前因子都同意表征相应的渐近单词的预测值。对于边缘纤维纤维调制，对数的前面因子在下部和上限上是不同的，并且随着调制的强度而平稳地变化。在准周期性哈珀模型的离域阶段中，对数负性的边界以及纠缠熵的边界的缩放与同质链的对数缩放率兼容。在本地化过渡时，上述纠缠特性的缩放是对数，但是与翻译不变的情况相比，预先因素大约降低了，大约是同一因素。
We study the scaling of logarithmic negativity between adjacent subsystems in critical fermion chains with various inhomogeneous modulations through numerically calculating its recently established lower and upper bounds. For random couplings, as well as for a relevant aperiodic modulation of the couplings, which induces an aperiodic singlet state, the bounds are found to increase logarithmically with the subsystem size, and both prefactors agree with the predicted values characterizing the corresponding asymptotic singlet state. For the marginal Fibonacci modulation, the prefactors in front of the logarithm are different for the lower and the upper bound, and vary smoothly with the strength of the modulation. In the delocalized phase of the quasi-periodic Harper model, the scaling of the bounds of the logarithmic negativity as well as that of the entanglement entropy are compatible with the logarithmic scaling of the homogeneous chain. At the localization transition, the scaling of the above entanglement characteristics holds to be logarithmic, but the prefactors are significantly reduced compared to those of the translationally invariant case, roughly by the same factor.
