Anisotropic-scaling localization in higher-dimensional non-Hermitian systems

TL;DR

This paper introduces anisotropic-scaling localization (ASL) in higher-dimensional non-Hermitian systems, revealing complex localization behaviors and mechanisms, and clarifying their spectral and boundary state characteristics.

Contribution

It uncovers the novel ASL phenomenon, providing analytical and numerical insights into its mechanisms and its distinction from edge skin states in higher-dimensional non-Hermitian systems.

Findings

ASL exhibits distinct size-dependent scaling in different directions.

ASL can originate from effective bulk couplings or 1D junctions.

Coexistence of loop-like spectra and skin-like boundary localization is explained.

Abstract

Spatial localization of quantum states is one of the focal points in condensed matter physics and quantum simulations, as it signatures profound physics such as nontrivial band topology and non-reciprocal non-Hermiticity. Yet, in higher dimensions, characterizing state localization becomes elusive due to the sophisticated interplay between different localization mechanisms and spacial geometries. In this work, we unveil an exotic type of localization phenomenon in higher-dimensional non-Hermitian systems, termed anisotropic-scaling localization (ASL), where localization lengths follow distinct size-dependent scaling rules in an anisotropic manner. Assisted with both analytical solution and numerical simulation, we find that ASL can emerge from two different mechanisms of effective bulk couplings or one-dimensional junction between different 1D edges, depending on how non-reciprocity is introduced to the system. The competition between ASL states and edge non-Hermitian skin states are further identified by their complex and real eigenenergies, respectively. Our results resolve the subtle co-existence of loop-like spectrum and skin-like localization of boundary states in contemporary literature, and provide a framework to classify the intricate higher-order non- Hermitian localization regarding their localization profiles.