This work introduces a new class of robust states known as Exceptional Boundary (EB) states, which are distinct from the well-known topological and non-Hermitian skin boundary states. EB states occur in the presence of exceptional points, which are non-Hermitian critical points where eigenstates coalesce and fail to span the Hilbert space. This eigenspace defectiveness not only limits the accessibility of state information, but also interplays with long-range order to give rise to singular propagators only possible in non-Hermitian settings. Their resultant EB eigenstates are characterized by robust anomalously large or negative occupation probabilities, unlike ordinary Fermi sea states whose probabilities lie between zero and one. EB states remain robust after a variety of quantum quenches and give rise to enigmatic negative entanglement entropy contributions. Through suitable perturbations, the coefficient of the logarithmic entanglement entropy scaling can be continuously tuned. EB states represent a new avenue for robustness arising from geometric defectiveness, independent of topological protection or non-reciprocal pumping.
This work introduces a new class of robust states known as Exceptional Boundary (EB) states, which are distinct from the well-known topological and non-Hermitian skin boundary states. EB states occur in the presence of exceptional points, which are non-Hermitian critical points where eigenstates coalesce and fail to span the Hilbert space. This eigenspace defectiveness not only limits the accessibility of state information, but also interplays with long-range order to give rise to singular propagators only possible in non-Hermitian settings. Their resultant EB eigenstates are characterized by robust anomalously large or negative occupation probabilities, unlike ordinary Fermi sea states whose probabilities lie between zero and one. EB states remain robust after a variety of quantum quenches and give rise to enigmatic negative entanglement entropy contributions. Through suitable perturbations, the coefficient of the logarithmic entanglement entropy scaling can be continuously tuned. EB states represent a new avenue for robustness arising from geometric defectiveness, independent of topological protection or non-reciprocal pumping.
This Letter introduces a new class of robust states known as exceptional bound (EB) states, which are distinct from the well-known topological and non-Hermitian skin boundary states. EB states occur in the presence of exceptional points, which are non-Hermitian critical points where eigenstates coalesce and fail to span the Hilbert space. This eigenspace defectiveness not only limits the accessibility of state information but also interplays with long-range order to give rise to singular propagators only possible in non-Hermitian settings. Their resultant EB eigenstates are characterized by robust anomalously large or negative occupation probabilities, unlike ordinary Fermi sea states whose probabilities lie between 0 and 1. EB states remain robust after a variety of quantum quenches and give rise to enigmatic negative entanglement entropy contributions. Through suitable perturbations, the coefficient of the logarithmic entanglement entropy scaling can be continuously tuned. EB states represent a new avenue for robustness arising from geometric defectiveness, independent of topological protection or nonreciprocal pumping.
Abstract The entanglement entropy encodes fundamental characteristics of quantum many‐body systems, and is particularly subtle in non‐Hermitian settings where eigenstates generically become non‐orthogonal. In this work, it is found that negative biorthogonal entanglement generically arises from topologically protected non‐orthogonal edge states in free fermion systems, especially for flat‐band edge states. Departing from previous literature which associated negative entanglement with exceptional gapless points, it is showed that robustly negative entanglement can still occur in gapped systems. Gapless 2D flat‐band edge states, however, exhibit novel entanglement behavior which scales quadratically with the transverse dimension L y , independent of system parameters. This dramatically negative scaling can be traced to a new mechanism known as non‐Hermitian critical skin compression (nHCSC), where topological and skin localization in one direction produces a hierarchy of extensively many probability non‐conserving entanglement eigenstates across a cut in another direction. This discovery sheds light on new avenues where topology interplays with criticality and non‐Hermitian localization, unrelated to traditional notions of topological entanglement entropy. This topologically protected negative entanglement also manifests in the second Rényi entropy, which can be measured through SWAP operator expectation values.
We investigate the entanglement properties of non-Hermitian Su-Schrieffer-Heeger (SSH) model from the perspective of the Generalized Brillouin Zone (GBZ). The non-Bloch entanglement entropy is defined on a quasi-reciprocal lattice, obtained by performing an ordinary Fourier transformation on the non-Bloch Hamiltonian. We demonstrate that the broken bulk-boundary correspondence is recovered in terms of the non-Bloch entanglement entropy. When the GBZ is circular, we show that the non-Bloch entanglement entropy is well-defined (real and positive-definite) in large parameter regions, except close to the exceptional points (EPs). In the critical region, we found that each Fermi point contributes precisely 1 to the central charge c of the logarithmic scaling. At the EP, the central charge becomes negative due to the presence of the exceptional bound state. For the case of non-circular GBZ, long-range hopping emerges in the quasi-reciprocal lattice, and the von Neumann entropy on the GBZ is no longer real. However, the non-Bloch edge entanglement entropy remains real, which serves as a reliable topological indicator and respects the bulk-boundary correspondence. We compute the topological phase diagram, and reveal the critical behavior along the exceptional phase boundaries.
This paper explores the novel concept of topological eigenvalues within the realm of non-Hermitian quantum mechanics, focusing on their role in unveiling spectral singularities. Unlike conventional Hermitian systems, non-Hermitian Hamiltonians, which describe open systems with gain and loss, exhibit complex eigenvalues and unique spectral features such as exceptional points (EPs) where eigenvalues and their corresponding eigenvectors coalesce. We introduce the idea that certain eigenvalues in non-Hermitian systems possess an inherent topological character, dictated by the geometry of the parameter space and the winding properties of the characteristic polynomial. These topological eigenvalues are shown to be intimately linked to spectral singularities, which are non-Hermitian generalizations of bound states in the continuum or points of perfect reflection/transmission, characterized by infinite scattering amplitudes. We develop a theoretical framework to identify and characterize these topological eigenvalues, demonstrating how they emerge from the interplay of non-Hermiticity and underlying symmetries. Our findings reveal that the robust nature of these topological eigenvalues provides a new lens through which to understand the exotic phenomena observed in non-Hermitian systems, including the non-Hermitian skin effect and the breakdown of traditional bulk-boundary correspondence. This work opens new avenues for designing robust non-Hermitian devices and understanding fundamental aspects of open quantum systems.
Open photonic systems provide a versatile platform for non-Hermitian physics, enabling control over complex spectra, transport, and light-matter interactions. Exceptional points (EPs), at which eigenvalues and eigenvectors coalesce and the governing operator becomes defective, play a central role because they combine branch-point spectral topology, nonanalytic perturbative response, and controllable eigenstate conversion. This Review provides a unified framework for EP photonics by systematically distinguishing exceptional degeneracies according to the underlying operator, spectral variable, boundary conditions, and experimentally accessible observables. We discuss Hamiltonian EPs, absorbing EPs associated with scattering zeros, real-frequency scattering-matrix and Jones-matrix EPs, Bloch and Floquet EPs, and Liouvillian EPs in open quantum systems. We review their spectral topology, static and dynamical encircling, higher-order exceptional structures, and coexistence with bound states in the continuum, together with applications in sensing, lasing, coherent absorption, directional scattering, polarization and wavefront control, nonlinear optics, optical storage, nonreciprocal photonics, and quantum photonics. We also critically assess the current limitations, practical challenges, and future perspectives of EP-based photonic technologies, with particular attention to robustness, noise, scalability, and experimentally measurable performance.
Exotic singular objects, known as exceptional points, are ubiquitous in non-Hermitian physics. They might be spectral singularities in energy bands that produce anomalous effects and defectiveness. The quantum entanglement of a generic non-Hermitian model with two different types of spectral exceptional points (SEPs) is systematically investigated in this paper. We discovered a relationship between non-unitary conformal field theories and the k-linear-type SEPs, which is typically associated with PT-symmetry or pesdo-Hermicity spontaneous breaking. The underlying association between k-square-root-type SEPs, which arise concurrently with real (imaginary) gap closing in the complex spectrum, mimicking first-order-phase-transition criticalities, and complex conformal field theories (cCFTs) is addressed through the calculation of complex central charges. From the entanglement spectrum, zero-energy exceptional modes are found to be distinct from normal zero modes or topological boundary modes. Finally, we include a brief discussion of analogous non-Hermitian quantum spin models and endeavor to establish an intuitive understanding of exceptional points through the spin picture in various scenarios.