论文标题
对广义的Aubry-André-Harper模型的持续同源分析
Persistent homology analysis of a generalized Aubry-André-Harper model
论文作者
论文摘要
由于需要分析可观察到的有限时间或尺寸缩放，因此在晶格模型中观察临界阶段是有挑战性的。我们研究持续同源性的计算拓扑技术如何用于表征广义的Aubry-André-Harper模型的阶段。使用持续同源性获得的特征的持续熵和平方平方寿命与常规措施（香农熵和反参与率）相似，并且可以区分局部，扩展和横向阶段。但是，我们发现持续的熵也清楚地将有序与该模型的无序政权区分开。持续的同源方法可以应用于能量本征态和波袋传播动力学。
Observing critical phases in lattice models is challenging due to the need to analyze the finite time or size scaling of observables. We study how the computational topology technique of persistent homology can be used to characterize phases of a generalized Aubry-André-Harper model. The persistent entropy and mean squared lifetime of features obtained using persistent homology behave similarly to conventional measures (Shannon entropy and inverse participation ratio) and can distinguish localized, extended, and crticial phases. However, we find that the persistent entropy also clearly distinguishes ordered from disordered regimes of the model. The persistent homology approach can be applied to both the energy eigenstates and the wavepacket propagation dynamics.
