Localization Landscape in Non-Hermitian and Floquet quantum systems

TL;DR

This paper extends the localization landscape theory to non-Hermitian, Floquet, and topological quantum systems, providing a geometric tool to predict localization phenomena without eigenstate computation.

Contribution

It introduces a generalized landscape based on $H^\u2212 H$ that predicts localization in diverse quantum systems, including driven and topological ones, with high accuracy.

Findings

Predicts localization without eigenstate calculation

Reveals spectral instabilities and skin effects

Accurately captures topological zero modes

Abstract

We propose a generalization of the Filoche--Mayboroda localization landscape that extends the theory well beyond the static, elliptic and Hermitian settings while preserving its geometric interpretability. Using the positive operator $H^\dagger H$, we obtain a landscape that predicts localization across non-Hermitian, Floquet, and topological systems without computing eigenstates. Singular-value collapse reveals spectral instabilities and skin effects, the Sambe formulation captures coherent destruction of tunneling, and topological zero modes emerge directly from the landscape. Applications to Hatano--Nelson chains, driven two-level systems, and driven Aubry--Andr\'e--Harper models confirm quantitative accuracy, establishing a unified predictor for localization in equilibrium and driven quantum matter.