In contrast with extended Bloch waves, a single particle can become spatially localized due to the so-called skin effect originating from non-Hermitian pumping. Here we show that in kinetically constrained many-body systems, the skin effect can instead manifest as dynamical amplification within the Fock space, beyond the intuitively expected and previously studied particle localization and clustering. We exemplify this non-Hermitian Fock skin effect in an asymmetric version of the PXP model and show that it gives rise to ergodicity-breaking eigenstates-the non-Hermitian analogs of quantum many-body scars. A distinguishing feature of these non-Hermitian scars is their enhanced robustness against external disorders. We propose an experimental realization of the non-Hermitian scar enhancement in a tilted Bose-Hubbard optical lattice with laser-induced loss. Additionally, we implement digital simulations of such scar enhancement on the IBM quantum processor. Our results show that the Fock skin effect provides a powerful tool for creating robust nonergodic states in generic open quantum systems.
In contrast with extended Bloch waves, a single particle can become spatially localized due to the so-called skin effect originating from non-Hermitian pumping. Here we show that in kinetically constrained many-body systems, the skin effect can instead manifest as dynamical amplification within the Fock space, beyond the intuitively expected and previously studied particle localization and clustering. We exemplify this non-Hermitian Fock skin effect in an asymmetric version of the PXP model and show that it gives rise to ergodicity-breaking eigenstates-the non-Hermitian analogs of quantum many-body scars. A distinguishing feature of these non-Hermitian scars is their enhanced robustness against external disorders. We propose an experimental realization of the non-Hermitian scar enhancement in a tilted Bose-Hubbard optical lattice with laser-induced loss. Additionally, we implement digital simulations of such scar enhancement on the IBM quantum processor. Our results show that the Fock skin effect provides a powerful tool for creating robust nonergodic states in generic open quantum 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.
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.
Abstract Quantum many-body scars (QMBSs) are atypical eigenstates in otherwise nonintegrable systems that weakly break ergodicity, exhibiting nonthermal dynamics and long-lived periodic revivals. However, implementing QMBS in non-Hermitian systems remains a significant challenge, as it demands a deep understanding of the influence of exceptional points (EPs) on quantum many-body dynamics, especially higher-order EPs. Here, we use single-photon interference to demonstrate that experimentally controlled non-Hermitian dissipation stabilizes and enhances scarred dynamics, realizing nearly perfect, high-fidelity revival. These ideas can be exemplified in quantum systems that support scarred dynamics. In the non-Hermitian regime, symmetry-promoted exceptional points confine the dynamics to robust nonthermal subspaces, enabling high-fidelity scarred revivals over an extended parameter range. These results establish non-Hermitian quantum engineering as a versatile strategy for creating and sustaining perfect quantum scars, offering pathways for quantum-enhanced metrology, coherent state preparation, and fault-tolerant quantum information processing.
Non-Hermiticity enables macroscopic accumulation of bulk states, named non-Hermitian skin effects. The non-Hermitian skin effects are well established for single-particle systems, but their proper characterization for general systems is elusive. Here, we propose a general criterion of non-Hermitian skin effects, which works for any finite-dimensional system evolved by a linear operator. The applicable systems include many-body systems and network systems. A system meeting the criterion exhibits enhanced non-normality of the evolution operator, accompanied by exceptional characteristics intrinsic to non-Hermitian systems. Applying the criterion, we discover a new type of non-Hermitian skin effect in many-body systems, which we dub the Fock space skin effect. We also discuss the Fock space skin effect-induced slow dynamics, which gives an experimental signal for the Fock space skin effect.
Abstract Criticality in non-Hermitian systems unveils unique phase transitions and scaling behaviors beyond Hermitian paradigms, offering new insights into the interplay between gain/loss, non-reciprocity, and complex energy spectra. In this paper, we uncover a new class of many-body critical non-Hermitian skin effect (CSE) originating from the interplay between multiple non-Hermitian pumping channels and Hubbard interactions. In particular, criticality in the real-to-complex transitions can selectively emerge within the subspace of bound states or scattering states, as well as their interacting admixtures. These mechanisms possess no single-particle analog and can be diagnosed through a specially defined correlation function. As more particles are involved, higher-order CSEs naturally arise, with greatly enhanced effective coupling strengths and hence greater experimental accessibility. Our results reveal an enriched landscape of non-Hermitian critical phenomena in interacting many-body systems, and pave the way for investigating unconventional non-Hermitian criticality in the context of various interaction-induced particle clustering configurations.
Thermalization in closed quantum systems and its breakdown are central to understanding the emergence of statistical behavior in isolated many-body systems. Kinetic constraints can hinder thermalization by restricting the allowed dynamics and giving rise to non-ergodic behavior. While various aspects of ergodicity breaking in kinetically constrained models have been extensively studied in Hermitian systems, their behavior in non-Hermitian kinetically constrained models remains less explored. In particular, the inequivalence of left and right eigenstate ensembles in non-Hermitian systems raises the question of whether they exhibit qualitatively different dynamical and eigenstate properties. In this work, we study non-Hermitian generalizations of the paradigmatic PXP and PPXPP models, focusing on their Krylov complexity, eigenstate structure, and dynamics. By exploiting the Arnoldi's algorithm, we find distinct behavior of Krylov complexity in the left and right eigenstate ensembles as non-Hermiticity is increased: in the right ensemble, it exhibits persistent oscillations with an increasing period, while in the left ensemble, it gradually saturates. The characteristic arch-shaped profile of the Arnoldi coefficients is also modified differently in the two ensembles, with a Hermitian-like arch re-emerging in the left ensemble at large non Hermiticity. Additionally, in the non-Hermitian PXP model, the right ensemble retains the characteristic scar structure, while the left ensemble develops additional non-scar eigenstates with anomalously low entanglement and large overlap with the vacuum state. These findings reveal that non-Hermiticity can affect Krylov dynamics and eigenstate structure differently in the left and right ensembles, demonstrating the need to treat them separately when characterizing non-Hermitian kinetically constrained systems.