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

Abstract

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.

Published version. 8 pages, 9 figures

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• Persistent homology of quantum entanglement
• Confinement in non-Abelian lattice gauge theory via persistent homology
• Magnetic Field Controlled Surface Localization of Spin-Wave Ferromagnetic Resonance Modes in 3D Nanostructures
• Topological Data Analysis of Monopole Current Networks in $U(1)$ Lattice Gauge Theory
• Topological data analysis of the deconfinement transition in SU(3) lattice gauge theory