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arXiv:2511.10156

Competing Localizations on Disordered Non-Hermitian Random Graph Lattice

S Rahul, A Harshitha

cond-mat.dis-nncond-mat.mes-hallquant-phSubmitted Nov 13, 2025• Announced Nov 14, 2025
v1 · Nov 13, 2025v2 · Nov 23, 2025
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Abstract

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 $Δ$, on site disorder $W$, and a random long-range coupling $p$ that render the underlying nature of random graph. By varying $p,$ $Δ$ and the disorder, we explore the interplay between topology, randomness, and non-Hermiticity in determining localization properties. Our results show the competition between skin effect driven and Anderson driven localizations in the parameter regimes. Despite the presence of large disorder, the skin effect driven localization coexists with Anderson driven localization.

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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 render the underlying nature of random graph. By varying p,p,p, ΔΔΔ and the disorder, we explore the interplay between topology, randomness, and non-Hermiticity in determining localization properties. Our results show the competition between skin effect driven and Anderson driven localizations in the parameter regimes. Despite the presence of large disorder, the skin effect driven localization coexists with Anderson driven localization.
The non-Hermitian systems exhibit extreme sensitivity to the boundary conditions. The change in the eigenspectrum with tuning boundary parameter is intimately connected to the non-Hermitian skin effect. The single-particle systems are affected by the boundary perturbations; however, the interplay of a random disorder potential and nonreciprocal hopping under boundary perturbations of an interacting many-body system is not yet clear. In this work, we examine the boundary sensitivity of a non-Hermitian interacting fermionic system in the presence of a random disorder potential. A nonzero boundary parameter results in real-complex spectral transitions with nonreciprocal (or unidirectional) hopping at weak disorder, while the many-body localization at strong disorder washes away real-complex transitions leading to dynamical stability and real eigenvalue spectrum. We show that the boundary-driven real-complex spectral transitions of the non-Hermitian chain are accompanied by the corresponding changes in the level statistics and nearest level-spacing distributions. The intriguing features of nonreciprocity and boundary sensitivity are further revealed using the averaged inverse participation ratios. Finally, we find distinct behavior in the quench dynamics of local particle density, population imbalance, and entanglement entropy of charge-density-wave ordered state that corroborate the real-complex and localization transitions. Our results provide a route to understanding disordered many-body systems under a generalized boundary.
Localization in one-dimensional interacting systems can be caused by disorder potentials or non-Hermiticity. The former phenomenon is the many-body localization (MBL), and the latter is the many-body non-Hermitian skin effect (NHSE). In this work, we numerically investigate the interplay between these two kinds of localization, where the energy-resolved MBL arises from a deterministic quasiperiodic potential in a fermionic chain. We propose a set of eigenstate properties and long-time dynamics that collectively distinguish the two localization mechanisms in the presence of non-Hermiticity. By computing the proposed diagnostics, we show that the thermal states are vulnerable to the many-body NHSE while the MBL states remain resilient up to a strong non-Hermiticity. Finally, we discuss experimental observables that probe the difference between the two localizations in a non-Hermitian quasiperiodic fermionic chain. Our results pave the way toward experimental observations on the interplay of interaction, quasiperiodic potential, and non-Hermiticity.
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.
The explorations of non-Hermiticity have been devoted to investigate the disorder-induced many-body localization (MBL). However, the sensitivity of the spatial boundary conditions and the interplay of the non-Hermitian skin effect with many-body phenomena are not yet clear. For a MBL system in the presence of nonreciprocal tunnelings and random disorder potential, we identify two different complex-real spectral transitions, one is present for both open and periodic boundaries while the other is present only for open boundaries of coupled non-Hermitian chains. The later is driven due to the interchain coupling at weak disorder where the level statistics of the real eigenenergy phase follows a Gaussian orthogonal ensemble. We further characterize wave functions through the (biorthogonal) inverse participation ratio and fractal dimension, which reveal the suppression of skin effect in the non-Hermitian MBL phase. Finally, we demonstrate that the quench dynamics of the local particle density, spin imbalance, and entanglement entropy also signify the hallmark of the boundary effects and nonergodic character of many-body localization.
The non-Hermitian skin effect (NHSE), which drives bulk states toward system boundaries, modifies bulk-boundary correspondence and complicates the identification of topological edge modes. Although breaking translational symmetry is known to influence this behavior, a systematic comparison of different structural classes remains limited. Here we investigate periodic, random, and quasiperiodic (Fibonacci) systems using a one-dimensional non-Hermitian quantum walk model. By matching the local scattering parameters in a topologically nontrivial regime, we isolate the role of spatial structure in the presence of the NHSE. We find that periodic systems exhibit pronounced boundary accumulation of bulk states. Random systems suppress this accumulation through Anderson localization, but the topological gap becomes partially filled with localized in-gap states. In contrast, the Fibonacci quasiperiodic system suppresses large-scale boundary accumulation while maintaining a well-defined topological gap. Analysis of the wave functions suggests that the hierarchical quasiperiodic structure fragments bulk states across multiple length scales, thereby mitigating the NHSE. These results identify deterministic quasiperiodicity as a distinct structural regime for controlling non-Hermitian skin dynamics and isolating topological boundary modes.
Recent years have witnessed a surge of research on the non-Hermitian skin effect (NHSE) in one-dimensional lattices with finite-range couplings. In this work, we show that the long-range couplings that decay as $1/{l}^{\ensuremath{\alpha}}$ at distance lll can fundamentally modify the behavior of NHSE and the scaling of quantum entanglement in the presence of nonreciprocity. At $\ensuremath{\alpha}=0$, the nonlocality of couplings gives rise to the scale-free skin modes, whose localization length is proportional to the system size. Increasing the exponent $\ensuremath{\alpha}$ drives a complex-to-real spectral transition and a crossover from a scalefree to constant localization length. Furthermore, the scaling of nonequilibrium steady-state entanglement entropy exhibits a subextensive law due to the nonlocality and the complex spectrum, in contrast to an area law arising from NHSE. Our results provide a theoretical understanding on the interplay between long-range couplings and non-Hermiticity.