Critical non-Hermitian skin effect

Linhu Li,Jiangbin Gong,Sen Mu,Ching Hua Lee

doi:10.1038/s41467-020-18917-4

Linhu Li, Jiangbin Gong + Show 2 more

Open Access

https://doi.org/10.1038/s41467-020-18917-4

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Journal: Nature Communications	Publication Date: Oct 30, 2020
Citations: 232	License type: open-access

Affiliation: National University of Singapore

Abstract

Critical systems represent physical boundaries between different phases of matter and have been intensely studied for their universality and rich physics. Yet, with the rise of non-Hermitian studies, fundamental concepts underpinning critical systems - like band gaps and locality - are increasingly called into question. This work uncovers a new class of criticality where eigenenergies and eigenstates of non-Hermitian lattice systems jump discontinuously across a critical point in the thermodynamic limit, unlike established critical scenarios with spectrum remaining continuous across a transition. Such critical behavior, dubbed the “critical non-Hermitian skin effect”, arises whenever subsystems with dissimilar non-reciprocal accumulations are coupled, however weakly. This indicates, as elaborated with the generalized Brillouin zone approach, that the thermodynamic and zero-coupling limits are not exchangeable, and that even a large system can be qualitatively different from its thermodynamic limit. Examples with anomalous scaling behavior are presented as manifestations of the critical non-Hermitian skin effect in finite-size systems. More spectacularly, topological in-gap modes can even be induced by changing the system size. We provide an explicit proposal for detecting the critical non-Hermitian skin effect in an RLC circuit setup, which also directly carries over to established setups in non-Hermitian optics and mechanics.

Highlights

Critical systems represent physical boundaries between different phases of matter and have been intensely studied for their universality and rich physics
Under open-boundary conditions (OBCs), eigenstates due to non-Hermitian skin effect (NHSE) can exponentially localize at a boundary, in contrast to Bloch states under periodic boundary conditions (PBCs)
The critical nonHermitian skin effect (CNHSE) heralds a whole class of discontinuous critical phase transitions with rich anomalous scaling behavior, challenging traditional associations of criticality with scale-free behavior

Summary

Introduction

Critical systems represent physical boundaries between different phases of matter and have been intensely studied for their universality and rich physics. This work uncovers a new class of criticality where eigenenergies and eigenstates of non-Hermitian lattice systems jump discontinuously across a critical point in the thermodynamic limit, unlike established critical scenarios with spectrum remaining continuous across a transition Such critical behavior, dubbed the “critical non-Hermitian skin effect”, arises whenever subsystems with dissimilar non-reciprocal accumulations are coupled, weakly. We uncover here a class of criticality, dubbed the “critical nonHermitian skin effect (CNHSE)”, where the eigenenergies and eigenstates in the thermodynamic limit “jump” between different skin solutions discontinuously across the critical point This is distinct from previously known phase transitions (Hermitian and non-Hermitian) (Fig. 1), where the eigenenergy spectrum can be continuously interpolated across the two bordering phases. Being strongly affected by minute perturbations around the critical point, such behavior may prove useful in sensing applications[41,42]

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