Abstract We investigate distinct non-Hermitian skin effects (NHSEs) in real and Fock spaces induced by the interplay between the Hilbert space fragmentation and multiple non-Hermitian pumping channels. Using an extended Hatano–Nelson model with next-nearest neighbor hopping and strong interaction as an example, we found that two fermions loaded in the lattice exhibit different real-space NHSE depending on the Hilbert space fragments to which they belong. Moreover, in the high-energy sector resulting from fragmentation, the two-particle-bound states form a one-dimensional lattice in Fock space, producing a Fock-space NHSE. At half-filling, richer patterns of Fock-space skin-like localization emerge for the different fragmented energy sectors and subsectors while real-space NHSE is suppressed by many-body effects. This study extends our understanding of the interplay between NHSE and Hilbert space fragmentation and provides detailed insights into their manifestation in interacting non-Hermitian systems.
Abstract We investigate distinct non-Hermitian skin effects (NHSEs) in real and Fock spaces induced by the interplay between the Hilbert space fragmentation and multiple non-Hermitian pumping channels. Using an extended Hatano–Nelson model with next-nearest neighbor hopping and strong interaction as an example, we found that two fermions loaded in the lattice exhibit different real-space NHSE depending on the Hilbert space fragments to which they belong. Moreover, in the high-energy sector resulting from fragmentation, the two-particle-bound states form a one-dimensional lattice in Fock space, producing a Fock-space NHSE. At half-filling, richer patterns of Fock-space skin-like localization emerge for the different fragmented energy sectors and subsectors while real-space NHSE is suppressed by many-body effects. This study extends our understanding of the interplay between NHSE and Hilbert space fragmentation and provides detailed insights into their manifestation in interacting non-Hermitian systems.
Various exotic many-body phenomena such as quantum scars and fractons have been linked to Hilbert space fragmentation. In this work, we find that in non-Hermitian settings, Hilbert space connectivity has an even more universal and fundamental influence, tightly controlling the nature of spectral amplification and state localization. Far more complicated than real-space lattices, non-Hermitian many-body Hilbert space graphs not only possess intricate competing amplification channels, but also global feedback loops connecting remote Fock states related by particle symmetry. These features lead to amplification behavior with unconventional scaling and localization properties. Particle occupation constraints can furthermore remove selected Hilbert space pathways, leading to robust unipolar and asymmetric bipolar skin localization in otherwise reciprocal processes. These results extend beyond simple interacting bosonic models and establish Hilbert space connectivity as a versatile control knob for many-body non-Hermitian critical transitions.
The non-Hermitian skin effect (NHSE) represents one of the most distinctive phenomena in non-Hermitian physics. Here, we uncover a new drag-induced NHSE mechanism in interacting Bose--Fermi mixtures where only bosons, but not fermions, experience asymmetric hopping.We show that strong Bose--Fermi interactions enable fermions to inherit boundary accumulation through correlated bound states.The interplay of interactions, quantum statistics, and non-Hermitian dynamics gives rise to an interaction-induced blockade mechanism, leading to highly asymmetric fermionic transport.We demonstrate that the drag-induced NHSE is dynamically stable and propose a feasible realization in ultracold Bose--Fermi mixtures with Floquet-engineered asymmetric tunneling.Our results establish a qualitatively distinct route to the NHSE, where non-Hermitian localization is not generated by direct nonreciprocal hopping of the localized particles themselves, but emerges through the interaction-mediated transfer of non-Hermitian dynamics between different quantum species. This mechanism further provides a potential route toward species-selective control of localization and transport in hybrid quantum matter.
Abstract Strong, non-perturbative interactions often lead to new exciting physics, as epitomized by emergent anyons from the Fractional Quantum hall effect. Within the actively investigated domain of non-Hermitian physics, we discover a new family of states known as non-Hermitian skin clusters. Taking distinct forms as Vertex, Topological, Interface, Extended and Localized skin clusters, they generically originate from asymmetric correlated hoppings on a lattice, in the strongly interacting limit with quenched single-body energetics. Distinct from non-Hermitian skin modes which accumulate at boundaries, our skin clusters are predominantly translation invariant particle clusters. As purely interacting phenomena, they fall outside the purview of generalized Brillouin zone analysis, although our effective lattice formulation provides alternative analytic and topological characterization. Non-Hermitian skin clusters fundamentally originate from the fragmentation structure of the Hilbert space, and may thus be of significant interest in modern many-body contexts like the ETH and quantum scars.
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 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.
We investigate the localization behavior of two-particle Hubbard model in the presence of non-reciprocal tunneling and non-Hermitian bound states can be obtained with strong repulsive interaction. Remarkably, the interaction induced bound state localization (BSL) can compete with non-Hermitian skin effect (NHSE) and give rise to diverse density profiles. Via the quantum scattering methods in the center of mass frame, the system can be mapped to an effective two dimensional (2D) lattice with the two-particle interaction contributing to a defective line. For the bound states of the largest eigen-energy, in contrast to the Hermitian cases, where the maximal localization center is pinned around the center of lattice, NHSE can lead to a faded diagonal line localization. For the unbound scattering states, unlike the single corner localization in the 2D Hatano-Nelson model, interaction can force the total localization to split into multiple centers. To make the system topological nontrivial, we further include terms taking the form of two-photon tunneling and the non-Hermitian photon bound pairs are also observed, which demonstrates a competition among NHSE, BSL and edge localization. Finally, we propose the experimental simulations via the platforms of electrical circuits. Our works shed light on the crossover study of quantum optics and non-Hermitian many body physics.