Directional dynamics of the non-Hermitian skin effect

Abstract

The dynamical consequences of the non-Hermitian skin effect (NHSE), while increasingly studied, have so far received less systematic attention than its now well-characterized static properties. Here we contribute to this developing front by applying quantum Liang information flow (QLIF)—an inherently directional measure of causal influence—to the non-Hermitian Su-Schrieffer-Heeger model with non-reciprocal hopping. Unlike symmetric correlation functions, QLIF directly captures the directional asymmetry {\mathbb{T}}_{R\to L}\ne {\mathbb{T}}_{L\to R} characteristic of non-reciprocal systems. We demonstrate a “scissors effect” where the asymmetry {\text{Δ}}_{\mathbb{T}} varies approximately linearly with the non-reciprocity parameter γ for small |γ|, and exhibits non-monotonic dependence on the skin length ξ, with optimal asymmetry at moderate skin localization. The velocity ordering ʋeff (γ < 0) &gt; ʋeff (0) > ʋeff (γ > 0) reveals NHSE-induced blocking of information flow against the skin direction. Three distinct temporal regimes emerge: light-cone-bounded spreading, γ-dependent stabilization, and coherent oscillations. These results establish the first quantitative connection between static skin localization and directional information dynamics, offering new insights into information propagation in non-reciprocal quantum systems.

Keywords

quantum information / non-Hermitian system / quantum causal relation

RIGHTS & PERMISSIONS

Higher Education Press 2026

Just Accepted

This article has successfully passed peer review and final editorial review, and will soon enter typesetting, proofreading and other publishing processes. The currently displayed version is the accepted final manuscript. The officially published version will be updated with format, DOI and citation information upon launch. We recommend that you pay attention to subsequent journal notifications and preferentially cite the officially published version. Thank you for your support and cooperation.