| 1. |
- Behrends, Jan, et al.
(författare)
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Transversal magnetotransport in Weyl semimetals : Exact numerical approach
- 2018
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Ingår i: Physical Review B. - 2469-9950 .- 2469-9969. ; 97:6
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Tidskriftsartikel (refereegranskat)abstract
- Magnetotransport experiments on Weyl semimetals are essential for investigating the intriguing topological and low-energy properties of Weyl nodes. If the transport direction is perpendicular to the applied magnetic field, experiments have shown a large positive magnetoresistance. In this work we present a theoretical scattering matrix approach to transversal magnetotransport in a Weyl node. Our numerical method confirms and goes beyond the existing perturbative analytical approach by treating disorder exactly. It is formulated in real space and is applicable to mesoscopic samples as well as in the bulk limit. In particular, we study the case of clean and strongly disordered samples.
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| 2. |
- Budich, Jan Carl, et al.
(författare)
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Symmetry-protected nodal phases in non-Hermitian systems
- 2019
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Ingår i: Physical Review B. - 2469-9950 .- 2469-9969. ; 99:4
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Tidskriftsartikel (refereegranskat)abstract
- Non-Hermitian (NH) Hamiltonians have become an important asset for the effective description of various physical systems that are subject to dissipation. Motivated by recent experimental progress on realizing the NH counterparts of gapless phases such as Weyl semimetals, here we investigate how NH symmetries affect the occurrence of exceptional points (EPs), that generalize the notion of nodal points in the spectrum beyond the Hermitian realm. Remarkably, we find that the dimension of the manifold of EPs is generically increased by one as compared to the case without symmetry. This leads to nodal surfaces formed by EPs that are stable as long as a protecting symmetry is preserved, and that are connected by open Fermi volumes. We illustrate our findings with analytically solvable two-band lattice models in one and two spatial dimensions, and show how they are readily generalized to generic NH crystalline systems.
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| 3. |
- Edvardsson, Elisabet, et al.
(författare)
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Non-Hermitian extensions of higher-order topological phases and their biorthogonal bulk-boundary correspondence
- 2019
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Ingår i: Physical Review B. - 2469-9950 .- 2469-9969. ; 99:8
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Tidskriftsartikel (refereegranskat)abstract
- Non-Hermitian Hamiltonians, which describe a wide range of dissipative systems, and higher-order topological phases, which exhibit novel boundary states on corners and hinges, comprise two areas of intense current research. Here we investigate systems where these frontiers merge and formulate a generalized biorthogonal bulk-boundary correspondence, which dictates the appearance of boundary modes at parameter values that are, in general, radically different from those that mark phase transitions in periodic systems. By analyzing the interplay between corner/hinge, edge/surface and bulk degrees of freedom we establish that the non-Hermitian extensions of higher-order topological phases exhibit an even richer phenomenology than their Hermitian counterparts and that this can be understood in a unifying way within our biorthogonal framework. Saliently this works in the presence of the non-Hermitian skin effect, and also naturally encompasses genuinely non-Hermitian phenomena in the absence thereof.
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| 4. |
- Edvardsson, Elisabet, et al.
(författare)
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Phase transitions and generalized biorthogonal polarization in non-Hermitian systems
- 2020
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Ingår i: Physical Review Research. - 2643-1564. ; 2:4
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Tidskriftsartikel (refereegranskat)abstract
- Non-Hermitian (NH) Hamiltonians can be used to describe dissipative systems, notably including systems with gain and loss, and are currently intensively studied in the context of topology. A salient difference between Hermitian and NH models is the breakdown of the conventional bulk-boundary correspondence, invalidating the use of topological invariants computed from the Bloch bands to characterize boundary modes in generic NH systems. One way to overcome this difficulty is to use the framework of biorthogonal quantum mechanics to define a biorthogonal polarization, which functions as a real-space invariant signaling the presence of boundary states. Here, we generalize the concept of the biorthogonal polarization beyond the previous results to systems with any number of boundary modes and show that it is invariant under basis transformations as well as local unitary transformations. Additionally, we focus on the anisotropic Su-Schrieffer-Heeger chain and study gap closings analytically. We also propose a generalization of a previously developed method with which to find all the bulk states of the system with open boundaries to NH models. Using the exact solutions for the bulk and boundary states, we elucidate genuinely NH aspects of the interplay between the bulk and boundary at the phase transitions.
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| 5. |
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| 6. |
- El Hassan, Ashraf, 1976-, et al.
(författare)
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Corner states of light in photonic waveguides
- 2019
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Ingår i: Nature Photonics. - : Springer Science and Business Media LLC. - 1749-4885 .- 1749-4893. ; 13:10, s. 697-700
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Tidskriftsartikel (refereegranskat)abstract
- The recently established paradigm of higher-order topological states of matter has shown that not only edge and surface states but also states localized to corners, can have robust and exotic properties. Here we report on the experimental realization of novel corner states made out of visible light in three-dimensional photonic structures inscribed in glass samples using femtosecond laser technology. By creating and analysing waveguide arrays, which form two-dimensional breathing kagome lattices in various sample geometries, we establish this as a platform for corner states exhibiting a remarkable degree of flexibility and control. In each sample geometry we measure eigenmodes that are localized at the corners in a finite frequency range, in complete analogy with a theoretical model of the breathing kagome. Here, measurements reveal that light can be ‘fractionalized,’ corresponding to simultaneous localization to each corner of a triangular sample, even in the presence of defects.
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| 7. |
- J. Bergholtz, Emil, et al.
(författare)
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Exceptional topology of non-Hermitian systems
- 2021
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Ingår i: Reviews of Modern Physics. - 0034-6861 .- 1539-0756. ; 93:1
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Forskningsöversikt (refereegranskat)abstract
- The current understanding of the role of topology in non-Hermitian (NH) systems and its far-reaching physical consequences observable in a range of dissipative settings are reviewed. In particular, how the paramount and genuinely NH concept of exceptional degeneracies, at which both eigenvalues and eigenvectors coalesce, leads to phenomena drastically distinct from the familiar Hermitian realm is discussed. An immediate consequence is the ubiquitous occurrence of nodal NH topological phases with concomitant open Fermi-Seifert surfaces, where conventional band-touching points are replaced by the aforementioned exceptional degeneracies. Furthermore, new notions of gapped phases including topological phases in single-band systems are detailed, and the manner in which a given physical context may affect the symmetry-based topological classification is clarified. A unique property of NH systems with relevance beyond the field of topological phases consists of the anomalous relation between bulk and boundary physics, stemming from the striking sensitivity of NH matrices to boundary conditions. Unifying several complementary insights recently reported in this context, a picture of intriguing phenomena such as the NH bulk-boundary correspondence and the NH skin effect is put together. Finally, applications of NH topology in both classical systems including optical setups with gain and loss, electric circuits, and mechanical systems and genuine quantum systems such as electronic transport settings at material junctions and dissipative cold-atom setups are reviewed.
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| 8. |
- Kunst, Flore K., et al.
(författare)
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Anatomy of topological surface states : Exact solutions from destructive interference on frustrated lattices
- 2017
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Ingår i: Physical Review B. - 2469-9950 .- 2469-9969. ; 96:8
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Tidskriftsartikel (refereegranskat)abstract
- The hallmark of topological phases is their robust boundary signature whose intriguing properties-such as the one-way transport on the chiral edge of a Chern insulator and the sudden disappearance of surface states forming open Fermi arcs on the surfaces of Weyl semimetals-are impossible to realize on the surface alone. Yet, despite the glaring simplicity of noninteracting topological bulk Hamiltonians and their concomitant energy spectrum, the detailed study of the corresponding surface states has essentially been restricted to numerical simulation. In this work, however, we show that exact analytical solutions of both topological and trivial surface states can be obtained for generic tight-binding models on a large class of geometrically frustrated lattices in any dimension without the need for fine-tuning of hopping amplitudes. Our solutions derive from local constraints tantamount to destructive interference between neighboring layer lattices perpendicular to the surface and provide microscopic insights into the structure of the surface states that enable analytical calculation of many desired properties including correlation functions, surface dispersion, Berry curvature, and the system size dependent gap closing, which necessarily occurs when the spatial localization switches surface. This further provides a deepened understanding of the bulkboundary correspondence. We illustrate our general findings on a large number of examples in two and three spatial dimensions. Notably, we derive exact chiral Chern insulator edge states on the spin-orbit-coupled kagome lattice, and Fermi arcs relevant for recently synthesized slabs of pyrochlore-based Eu2Ir2O7 and Nd2Ir2O7, which realize an all-in-all-out spin configuration, as well as for spin-ice-like two-in-two-out and one-in-three-out configurations, which are both relevant for Pr2Ir2O7. Remarkably, each of the pyrochlore examples exhibit clearly resolved Fermi arcs although only the one-in-three-out configuration features bulk Weyl nodes in realistic parameter regimes. Our approach generalizes to symmetry protected phases, e.g., quantum spin Hall systems and Dirac semimetals with time-reversal symmetry, and can furthermore signal the absence of topological surface states, which we illustrate for a class of models akin to the trivial surface of Hourglass materials KHgX where the exact solutions apply but, independently of Hamiltonian details, yield eigenstates delocalized over the entire sample.
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| 9. |
- Kunst, Flore K., et al.
(författare)
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Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems
- 2018
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Ingår i: Physical Review Letters. - 0031-9007 .- 1079-7114. ; 121:2
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Tidskriftsartikel (refereegranskat)abstract
- Non-Hermitian systems exhibit striking exceptions from the paradigmatic bulk-boundary correspondence, including the failure of bulk Bloch band invariants in predicting boundary states and the (dis) appearance of boundary states at parameter values far from those corresponding to gap closings in periodic systems without boundaries. Here, we provide a comprehensive framework to unravel this disparity based on the notion of biorthogonal quantum mechanics: While the properties of the left and right eigenstates corresponding to boundary modes are individually decoupled from the bulk physics in non-Hermitian systems, their combined biorthogonal density penetrates the bulk precisely when phase transitions occur. This leads to generalized bulk-boundary correspondence and a quantized biorthogonal polarization that is formulated directly in systems with open boundaries. We illustrate our general insights by deriving the phase diagram for several microscopic open boundary models, including exactly solvable non-Hermitian extensions of the Su-Schrieffer-Heeger model and Chern insulators.
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| 10. |
- Kunst, Flore K., et al.
(författare)
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Boundaries of boundaries : A systematic approach to lattice models with solvable boundary states of arbitrary codimension
- 2019
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Ingår i: Physical Review B. - 2469-9950 .- 2469-9969. ; 99:8
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Tidskriftsartikel (refereegranskat)abstract
- We present a generic and systematic approach for constructing D−dimensional lattice models with exactly solvable d−dimensional boundary states localized to corners, edges, hinges, and surfaces. These solvable models represent a class of “sweet spots” in the space of possible tight-binding models—the exact solutions remain valid for any tight-binding parameters as long as they obey simple locality conditions that are manifest in the underlying lattice structure. Consequently, our models capture the physics of both (higher order) topological and nontopological phases as well as the transitions between them in a particularly illuminating and transparent manner.
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| 11. |
- Kunst, Flore K., et al.
(författare)
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Extended Bloch theorem for topological lattice models with open boundaries
- 2019
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Ingår i: Physical Review B. - 2469-9950 .- 2469-9969. ; 99:8
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Tidskriftsartikel (refereegranskat)abstract
- While the Bloch spectrum of translationally invariant noninteracting lattice models is trivially obtained by a Fourier transformation, diagonalizing the same problem in the presence of open boundary conditions is typically only possible numerically or in idealized limits. Here we present exact analytic solutions for the boundary states in a number of lattice models of current interest, including nodal-line semimetals on a hyperhoneycomb lattice, spin-orbit coupled graphene, and three-dimensional topological insulators on a diamond lattice, for which no previous exact finite-size solutions are available in the literature. Furthermore, we identify spectral mirror symmetry as the key criterium for analytically obtaining the entire (bulk and boundary) spectrum as well as the concomitant eigenstates, and exemplify this for Chern and Z2 insulators with open boundaries of codimension one. In the case of the two-dimensional Lieb lattice, we extend this further and show how to analytically obtain the entire spectrum in the presence of open boundaries in both directions, where it has a clear interpretation in terms of bulk, edge, and corner states.
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| 12. |
- Kunst, Flore K., et al.
(författare)
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Lattice models with exactly solvable topological hinge and corner states
- 2018
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Ingår i: Physical Review B. - 2469-9950 .- 2469-9969. ; 97:24
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Tidskriftsartikel (refereegranskat)abstract
- We devise a generic recipe for constructing D-dimensional lattice models whose d-dimensional boundary states, located on surfaces, hinges, corners, and so forth, can be obtained exactly. The solvability is rooted in the underlying lattice structure and as such does not depend on fine tuning, allowing us to track their evolution throughout various phases and across phase transitions. Most saliently, our models provide boundary solvable examples of the recently introduced higher-order topological phases. We apply our general approach to breathing and anisotropic kagome and pyrochlore lattices for which we obtain exact corner eigenstates, and to periodically driven two-dimensional models as well as to three-dimensional lattices where we present exact solutions corresponding to one-dimensional chiral states at the hinges of the lattice. We relate the higher-order topological nature of these models to reflection symmetries in combination with their provenance from lower-dimensional conventional topological phases.
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| 13. |
- Kunst, Flore K., et al.
(författare)
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Non-Hermitian systems and topology : A transfer-matrix perspective
- 2019
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Ingår i: Physical Review B. - 2469-9950 .- 2469-9969. ; 99:24
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Tidskriftsartikel (refereegranskat)abstract
- Topological phases of Hermitian systems are known to exhibit intriguing properties such as the presence of robust boundary states and the famed bulk-boundary correspondence. These features can change drastically for their non-Hermitian generalizations, as exemplified by a general breakdown of bulk-boundary correspondence and a localization of all states at the boundary, termed the non-Hermitian skin effect. In this paper, we present a completely analytical unifying framework for studying these systems using generalized transfer matrices, a real-space approach suitable for systems with periodic as well as open boundary conditions. We show that various qualitative properties of these systems can be easily deduced from the transfer matrix. For instance, the connection between the breakdown of the conventional bulk-boundary correspondence and the existence of a non-Hermitian skin effect, previously observed numerically, is traced back to the transfer matrix having a determinant not equal to unity. The vanishing of this determinant signals real-space exceptional points, whose order scales with the system size. We also derive previously proposed topological invariants such as the biorthogonal polarization and the Chern number computed on a complexified Brillouin zone. Finally, we define an invariant for and thereby clarify the meaning of topologically protected boundary modes for non-Hermitian systems.
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| 14. |
- Sayyad, Sharareh, et al.
(författare)
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Symmetry-protected exceptional and nodal points in non-Hermitian systems
- 2023
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Ingår i: SciPost Physics. - 2542-4653. ; 15:5
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Tidskriftsartikel (refereegranskat)abstract
- One of the unique features of non-Hermitian (NH) systems is the appearance of NH degeneracies known as exceptional points (EPs). The extensively studied defective EPs occur when the Hamiltonian becomes non-diagonalizable. Aside from this degeneracy, we show that NH systems may host two further types of non-defective degeneracies, namely, non-defective EPs and ordinary (Hermitian) nodal points. The non-defective EPs manifest themselves by i) the diagonalizability of the NH Hamiltonian at these points and ii) the non-diagonalizability of the Hamiltonian along certain intersections of these points, resulting in instabilities in the Jordan decomposition when approaching the points from certain directions. We demonstrate that certain discrete symmetries, namely parity-time, parity-particle-hole, and pseudo-Hermitian symmetry, guarantee the occurrence of both defective and non-defective EPs. We extend this list of symmetries by including the NH time-reversal symmetry in two-band systems. Two-band and four-band models exemplify our findings. Through an example, we further reveal that ordinary nodal points may coexist with defective EPs in NH models when the above symmetries are relaxed.
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| 15. |
- Sayyad, Sharareh, et al.
(författare)
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Symmetry-protected exceptional and nodal points in non-Hermitian systems
- 2023
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Ingår i: SciPost Physics. - : Stichting SciPost. - 2542-4653. ; 15:5
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Tidskriftsartikel (refereegranskat)abstract
- One of the unique features of non-Hermitian (NH) systems is the appearance of NH degeneracies known as exceptional points (EPs). The extensively studied defective EPs occur when the Hamiltonian becomes non-diagonalizable. Aside from this degeneracy, we show that NH systems may host two further types of non-defective degeneracies, namely, non-defective EPs and ordinary (Hermitian) nodal points. The non-defective EPs manifest themselves by i) the diagonalizability of the NH Hamiltonian at these points and ii) the non-diagonalizability of the Hamiltonian along certain intersections of these points, resulting in instabilities in the Jordan decomposition when approaching the points from certain directions. We demonstrate that certain discrete symmetries, namely parity-time, parity-particle-hole, and pseudo-Hermitian symmetry, guarantee the occurrence of both defective and non-defective EPs. We extend this list of symmetries by including the NH time-reversal symmetry in two-band systems. Two-band and four-band models exemplify our findings. Through an example, we further reveal that ordinary nodal points may coexist with defective EPs in NH models when the above symmetries are relaxed.
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| 16. |
- Stålhammar, Marcus, 1994-, et al.
(författare)
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PT symmetry-protected exceptional cones and analogue Hawking radiation
- 2023
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Ingår i: New Journal of Physics. - : IOP Publishing. - 1367-2630. ; 25:4
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Tidskriftsartikel (refereegranskat)abstract
- Non-Hermitian Hamiltonians, which effectively describe dissipative systems, and analogue gravity models, which simulate properties of gravitational objects, comprise seemingly different areas of current research. Here, we investigate the interplay between the two by relating parity-time-symmetric dissipative Weyl-type Hamiltonians to analogue Schwarzschild black holes emitting Hawking radiation. We show that the exceptional points of these Hamiltonians form tilted cones mimicking the behavior of the light cone of a radially infalling observer approaching a black hole horizon. We further investigate the presence of tunneling processes, reminiscent of those happening in black holes, in a concrete example model. We interpret the non-trivial result as the purely thermal contribution to analogue Hawking radiation in a Schwarzschild black hole. Assuming that our particular Hamiltonian models a photonic crystal, we discuss the concrete nature of the analogue Hawking radiation in this particular setup.
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| 17. |
- Terrier, Fanny, et al.
(författare)
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Dissipative analog of four-dimensional quantum Hall physics
- 2020
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Ingår i: Physical Review Research. - 2643-1564. ; 2:2
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Tidskriftsartikel (refereegranskat)abstract
- Four-dimensional quantum Hall (QH) models usually rely on synthetic dimensions for their simulation in experiment. Here, we study a QH system which features a nontrivial configuration of three-dimensional Weyl cones on its boundaries. We propose a three-dimensional analog of this model in the form of a dissipative Weyl semimetal (WSM) described by a non-Hermitian (NH) Hamiltonian, which in the long-time limit manifests the anomalous boundary physics of the four-dimensional QH model in the bulk spectrum. The topology of the NH WSM is captured by a three-dimensional winding number whose value is directly related to the total chirality of the surviving Weyl nodes. Upon taking open boundary conditions, instead of Fermi arcs, we find exceptional points with an order that scales with system size.
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