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.
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 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.
In the present study, the interplay among interaction, topology, quasiperiodicity, and non-Hermiticity is studied. The hard-core bosons model on a one-dimensional lattice with asymmetry hoppings and quasiperiodic onsite potentials is selected. This model, which preserves time-reversal symmetry (TRS), will exhibit three types of phase transition: Real-complex transition of eigenenergies, topological phase transition, and many-body localization (MBL) phase transition. For the real-complex transition, it is found that the imaginary parts of the eigenenergies are always suppressed by the MBL. Moreover, by calculating the winding number, a topological phase transition can be revealed with the increase of potential amplitude, and we find that the behavior is quite different from the single-particle systems. Based on our numerical results, we conjecture that these three types of phase transition occur at the same point in the thermodynamic limit, and the MBL transition of quasiperiodic system and disordered system should belong to different universality classes. Finally, we demonstrate that these phase transitions can profoundly affect the dynamics of the non-Hermitian many-body system.
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.
We investigate the fate of a many-body localized phase in a non-Hermitian quasiperiodic model of hardcore bosons subjected to periodic driving. While in general, the many-body localized system is known to thermalize with increasing driving period due to Floquet heating, in this case, we demonstrate that the initially localized system first delocalizes and then localizes again, resulting in a re-entrant many-body localization (MBL) transition as a function of the driving period. Strikingly, further increase in the driving period results in a series of localization-delocalization transitions leaving behind traces of extended regimes (islands) in between MBL phases. Furthermore, non-Hermiticity renders the extended islands boundary-sensitive, resulting in a Floquet many-body skin effect under open boundaries. We present numerical evidence from spectral and dynamic studies, confirming these findings. Our study opens new pathways for understanding the interplay between non-Hermiticity and quasiperiodicity in driven systems.
The non-Hermitian skin effect (NHSE) is a fascinating phenomenon in nonequilibrium systems where eigenstates massively localize at the systems’ boundaries, pumping (quasi-)particles loaded in these systems unidirectionally to the boundaries. Its interplay with many-body effects has been widely explored recently, and inter-particle repulsion or Fermi degeneracy pressure have been shown to limit the boundary accumulation induced by the NHSE both in their eigensolutions and dynamics. However, in this work we find that anyonic statistics can even more profoundly affect the NHSE dynamics, suppressing or even reversing the state dynamics against the localizing direction of the NHSE. This phenomenon is found to be more pronounced when more particles are involved. The spreading of quantum information in this system shows even more exotic phenomena, where NHSE affects only the information dynamics for a thermal ensemble, but not that for a single initial state. Our results open up a new avenue on exploring novel non-Hermitian phenomena arisen from the interplay between NHSE and anyonic statistics, and can potentially be demonstrated in ultracold atomic quantum simulators and quantum computers. Anyons are a general class of particles with unusual statistics beyond conventional bosons and fermions. In this work, the authors reveal that anyonic statistics can profoundly affect the non-Hermitian skin effect (NHSE) dynamically, suppressing or even reversing the NHSE-induced unidirectional evolution of both state dynamics and quantum information spreading, while keeping qualitatively the same skin-localization of static eigensolutions.
The non-Hermitian skin effect (NHSE), featured by the collapse of bulk-band eigenstates into the localized boundary modes of the systems, is one of most striking properties in the fields of non-Hermitian physics. Unique physical phenomena related to the NHSE have attracted a lot of interest, however, their experimental realizations usually require nonreciprocal hopping, which faces a great challenge in ultracold-atom systems. In this work, we propose to realize the NHSE in a 1D optical lattice by periodically-driven ultracold atoms in the presence of staggered atomic loss. By studying the effective Floquet Hamiltonian in the high-frequency approximation, we reveal the underlying mechanism for the periodic-driving-induced the NHSE. We found that the robust NHSE can be tuned by driving phase, which is manifested by the dynamical localization. Most remarkably, we uncover the periodic-driving-induced critical skin effect for two coupled chains with different driving phases, accompanied by the appearance of size-dependent topological in-gap modes. Our studies provide a feasible way for observing the NHSE and exploring corresponding unique physical phenomena due to the interplay of non-Hermiticity and many-body statistics in ultracold-atom systems.