Persistent homology analysis of a generalized Aubry-Andr\'{e}-Harper model

TL;DR

This paper demonstrates how persistent homology, a computational topology method, can effectively identify and distinguish different phases, including localized, extended, critical, ordered, and disordered regimes, in a generalized Aubry-Andre9-Harper model.

Contribution

The study introduces persistent homology as a novel tool for phase characterization in lattice models, showing its effectiveness in identifying various phases and regimes.

Findings

Persistent entropy and mean squared lifetime correlate with traditional measures.

Persistent homology distinguishes localized, extended, and critical phases.

It also clearly separates ordered from disordered regimes.

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-Andr\'{e}-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.