Persistent homology analysis of a generalized Aubry-André-Harper model

Observing critical phases in lattice models is challenging due to the need analyze finite time or size scaling of observables. We study how computational topology technique persistent homology can be used characterize a generalized Aubry-Andr\'e-Harper model. The entropy and mean squared lifetime features obtained using behave similarly conventional measures (Shannon inverse participation ratio) distinguish localized, extended, phases. However, we find that also clearly distinguishes ordered from disordered regimes approach applied both energy eigenstates wave packet propagation dynamics.