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arXiv:2512.24107

Entanglement dynamics driven by topology and non-Hermiticity

Li-Wei Wang, Bolun Hu, Haixiao Zhang, Kefan Sun, Ying Cheng, Jian-Hua Jiang

physics.opticscond-mat.mes-hallquant-phSubmitted Dec 30, 2025• Announced Dec 31, 2025
arXivHTMLPDF

Abstract

The interplay between topology and non-Hermiticity gives rise to exotic dynamic phenomena that challenge conventional wave-packet propagation and entanglement dynamics. While recent studies have established the non-Hermitian skin effect (NHSE) as a key mechanism for anomalous wave dynamics, a unified framework for characterizing and controlling entanglement evolution in non-Hermitian topological systems remains underdeveloped. Here, by combining theory and experiments, we demonstrate that entanglement entropy (EE) and transport currents serve as robust dynamic probes to distinguish various non-Hermitian topological regimes. Using a generalized non-Hermitian Su-Schrieffer-Heeger model implemented in an acoustic analog platform, we identify three dynamic phases, bulk-like, edge-like, and skin-like regimes, each exhibiting unique EE signatures and transport characteristics. In particular, skin-like dynamics exhibit periodic information shuttling with finite, oscillatory EE, while edge-like dynamics lead to complete EE suppression. We further map the dynamic phase diagram and show that EE scaling and temporal profiles directly reflect the competition between coherent delocalization and NHSE-driven localization. Our results establish a programmable approach to steering entanglement and transport via tailored non-Hermitian couplings, offering a pathway for engineering quantum information dynamics in synthetic phononic, photonic, and quantum simulators.

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The interplay between topology and non-Hermiticity gives rise to exotic dynamic phenomena that challenge conventional wave-packet propagation and entanglement dynamics. While recent studies have established the non-Hermitian skin effect (NHSE) as a key mechanism for anomalous wave dynamics, a unified framework for characterizing and controlling entanglement evolution in non-Hermitian topological systems remains underdeveloped. Here, by combining theory and experiments, we demonstrate that entanglement entropy (EE) and transport currents serve as robust dynamic probes to distinguish various non-Hermitian topological regimes. Using a generalized non-Hermitian Su-Schrieffer-Heeger model implemented in an acoustic analog platform, we identify three dynamic phases, bulk-like, edge-like, and skin-like regimes, each exhibiting unique EE signatures and transport characteristics. In particular, skin-like dynamics exhibit periodic information shuttling with finite, oscillatory EE, while edge-like dynamics lead to complete EE suppression. We further map the dynamic phase diagram and show that EE scaling and temporal profiles directly reflect the competition between coherent delocalization and NHSE-driven localization. Our results establish a programmable approach to steering entanglement and transport via tailored non-Hermitian couplings, offering a pathway for engineering quantum information dynamics in synthetic phononic, photonic, and quantum simulators.
Abstract The characterization of topological phases in disordered non-Hermitian systems remains a formidable challenge, as the non-Hermitian skin effect (NHSE) disrupts the conventional bulk-boundary correspondence and renders spectral invariants unreliable. In this letter, we propose the real part of the biorthogonal entanglement entropy as a precise, basis-independent diagnostic that cuts through this complexity. Investigating a disordered non-reciprocal Kitaev chain, we demonstrate that this entropic probe provides a robust, boundary-sensitive diagnostic that faithfully tracks the topological phase transition even in regimes where traditional winding numbers fluctuate wildly. Crucially, we uncover an anomalous critical scaling of the entanglement entropy: while the Hermitian limit follows standard conformal scaling , the non-Hermitian critical point exhibits a super-critical effective central charge of . Within the studied system sizes , this enhancement is consistent with skin-effect–driven non-unitary behavior at the critical point. Our findings establish biorthogonal entanglement not only as a robust order parameter for the topological Anderson insulator but also as an experimentally accessible signature in topo-electric circuits.
The non-Hermitian skin effect (NHSE), the accumulation of eigen-wave functions at boundaries of open systems, underlies a variety of exotic properties that defy conventional wisdom. While the NHSE and its intriguing impact on band topology and dynamics have been observed in classical or photonic systems, their demonstration in a quantum gas system remains elusive. Here we report the experimental realization of a dissipative Aharonov-Bohm chain-non-Hermitian topological model with NHSE-in the momentum space of a two-component Bose-Einstein condensate. We identify signatures of the NHSE in the condensate dynamics, and perform Bragg spectroscopy to resolve topological edge states against a background of localized bulk states. Our Letter sets the stage for further investigation on the interplay of many-body statistics and interactions with the NHSE, and is a significant step forward in the quantum control and simulation of non-Hermitian physics.
The non-Hermitian skin effect (NHSE) refers to the accumulation of an extensive number of eigenstates at system boundaries under open boundary conditions (OBCs). As a dynamical consequence, wave packets in such systems drift and ultimately accumulate at a boundary, giving rise to the dynamical skin effect (DSE). While strong quasiperiodic potentials are known to suppress the DSE by inducing localization, we show that the introduction of Ornstein-Uhlenbeck (OU) noise unexpectedly restores it. Using perturbative analysis, we demonstrate that noise effectively maps the non-Hermitian Schrödinger dynamics onto a non-reciprocal master equation, whose complex spectrum develops a noise-induced point gap. This mechanism enables delocalization, reinstates directional transport, and revives the DSE even in regimes where the static NHSE is absent. Moreover, the relaxation dynamics exhibit a non-monotonic dependence on noise strength, reflecting a competition between noise-assisted delocalization and noise-induced decoherence. Our results uncover a noise-enabled mechanism for resurrecting the DSE and suggest a new route for controlling transport in quasiperiodic, open quantum systems.
Recent years have seen remarkable development in open quantum systems effectively described by non-Hermitian Hamiltonians. A unique feature of non-Hermitian topological systems is the skin effect, anomalous localization of an extensive number of eigenstates driven by nonreciprocal dissipation. Despite its significance for non-Hermitian topological phases, the relevance of the skin effect to quantum entanglement and critical phenomena has remained unclear. Here, we find that the skin effect induces a nonequilibrium quantum phase transition in the entanglement dynamics. We show that the skin effect gives rise to a macroscopic flow of particles and suppresses the entanglement propagation and thermalization, leading to the area law of the entanglement entropy in the nonequilibrium steady state. Moreover, we reveal an entanglement phase transition induced by the competition between the unitary dynamics and the skin effect even without disorder or interactions. This entanglement phase transition accompanies nonequilibrium quantum criticality characterized by a nonunitary conformal field theory whose effective central charge is extremely sensitive to the boundary conditions. We also demonstrate that it originates from an exceptional point of the non-Hermitian Hamiltonian and the concomitant scale invariance of the skin modes localized according to the power law. Furthermore, we show that the skin effect leads to the purification and the reduction of von Neumann entropy even in Markovian open quantum systems described by the Lindblad master equation. Our work opens a way to control the entanglement growth and establishes a fundamental understanding of phase transitions and critical phenomena in open quantum systems far from thermal equilibrium.
Non-Hermitian many-body physics reveals a rich interplay between topology, localization, and boundary effects, yet their collective behavior in interacting disordered systems remains largely unexplored. In this work, we study an interacting non-Hermitian spin chain subject to a quasi-periodic longitudinal field, providing a unified and controlled setting, where non-Hermitian dynamics, interactions, and localization mechanisms intertwine. Remarkably, we discover a "D-shaped" many-body mobility edge that separates extended and localized eigenstates, while simultaneously delineating regimes of many-body localization and the many-body skin effect (where many-body eigenstates acquire an anomalous drift towards a boundary under open boundaries) emerging from the combined action of interactions, non-Hermiticity, and driving amplitude. We demonstrate that the skin effect induces multifractal scaling in the non-Hermitian eigenstates, providing a clear signature of the many-body skin effect. Employing diagnostics such as the fractal dimension, complex eigenvalue fractions, and many-body inverse participation ratios, we map out a unified phase diagram in which all measures consistently identify the "D-shaped" mobility edge. Finally, we probe this interplay using both complex level-spacing statistics and dynamical observables such as density imbalance, entanglement growth, and wave-packet evolution, culminating in a rich many-body mobility phase diagram that captures both the many-body skin effect and localization transitions. Our results identify a clear, defining signature of the "D-shaped" many-body mobility edge, and underscore its pivotal role in shaping the physics of open quantum many-body systems.
Phase transitions in one-dimensional lattice systems are well established and have been extensively studied within both Hermitian and non-Hermitian frameworks. In this work, we extend this understanding to a more general setting by investigating localization and delocalization transitions and the behavior of the non-Hermitian skin effect (NHSE) using a tight-binding model on a generalized random graph lattice. Our model incorporates three key parameters, asymmetric hopping ΔΔΔ, on-site disorder WWW, and a random long-range coupling ppp that together define the underlying random graph structure. By varying ppp, ΔΔΔ, and the disorder strength, we explore the interplay between topology, randomness, and non-Hermiticity in determining localization properties. Our results show a strong competition between skin effect driven and Anderson driven localizations across parameter regimes. Notably, even in the presence of strong disorder, skin effect driven localization coexists with Anderson-driven localization. We further discuss the relevance of these results to machine-learning architectures and information propagation in complex networks and other real-world problems.