In this paper, we provide a topological classification of isolated EPs based on homotopy theory. First, we show that various topological phases stem from a geometric phase. First, we show that various topological phases stem from a geometric phase. The direction of the EL can be identified by the corresponding Berry curvature. In one dimension, it was recently noted theoretically and demonstrated experimentally that the eigenvalue topology is classified by the braid group. The signatures of this phase are two pairs of Kramers degenerate Floquet quasienergy bands that are separated by an imaginary gap. 6. correspondence in the non-Hermitian version [48], and non-Hermitian skin effect [49]. 1, which consists of one pair of identical fiber Bragg gratings (FBGs) operating around 1550 n m with a bandwidth of 7 n m. E r 3 + - and C e 3 +-doped phosphosilicate sol-gel can be coated on the facets of each FBG to serve as active and lossy materials, respectively. The appearance of the degenerate . Publication. . We review 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.
. . We propose an anti-parity-time (anti-$\\mathcal{PT}$) symmetric non-Hermitian Su-Schrieffer-Heeger (SSH) model, where the large non-Hermiticity constructively creates nontrivial topology and greatly expands the topological phase. Their synergy will.
The authors formulate a homotopy classification and knot theory of exceptional points and present a non-Hermitian no-go theorem governing the possible configurations of exceptional points and their splitting rules on a two-dimensional lattice. Februar 2021 Publication 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. It describes the phenomenon where an extensive number of boundary modes appears under the open boundary conditions in a non-Hermitian system. The generalization of the Chern number to non-Hermitian Hamiltonians initiated this reexamination; however, there is no established connection between a non-Hermitian topological Then we review topological classifications in terms of the ten-fold Altland-Zirnbauer symmetry class. Non-Hermitian topology in evolutionary game theory: Exceptional points and skin effects in rock-paper-scissors cycles Tsuneya Yoshida, Tomonari Mizoguchi, Yasuhiro Hatsugai Submitted on 2021-09-22. Their topological structures called point-gap topology3-5 are unique to non-Hermitian systems. Band structure in the lossless (real-valued) and lossy (left, real part; right, imaginary part) cases. [] For dissipative systems, the associated eigenspectra are functions of the dissipation rates and an EP occurs at a critical dissipation rate c $\Gamma _c$ around which the real and imaginary part of two or more eigenvalues coalesce and bifurcate, respectively. In particular, we elucidate how the paramount and genuinely NH concept of exceptional degeneracies, at which both .
Their synergy will further produce more exotic topological effects in synthetic matter. 10 (QGT), which includes the Berry curvature (the cornerstone of Hermi- 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. Initial interest revolved around exceptional points exhibiting unique topological features with no counterparts in Hermitian systems, such as Weyl exceptional rings [60], bulk Fermi arcs The generalization of inversion symmetry is unique to non-Hermitian systems. The transport channels occur due to a Z 2 non-Hermitian Floquet topological phase that is protected by time-reversal symmetry. Non-Hermitian skin effects and exceptional points are topological phenomena characterized by integer winding numbers. Special attentions are given to exceptional points - branch-point singularities on the complex eigenvalue manifolds that exhibit non-trivial topological properties.
Namely, under a change of a system parameter, the GBZ is deformed so that The search for topological states in non-Hermitian systems, and more specifically in non-Hermitian lattice models, has become a newly emerging research front.Non-Hermitian systems are much more than a theoretical curiosity, they arise naturally in the description of the finite lifetime due to interactions, or more prominently, in photonic or acoustic systems. 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. 1a). In particular, how the paramount and genuinely NH concept of exceptional degeneracies, at which both eigenvalues and eigenvectors . Mapping between Non-Hermitian Quantum and Classical Models The non-Hermitian topology contained in the model of Eq. Abstract. Schematic diagram of the proposed non-Hermitian system based on coupled Fabry-Prot microcavities is illustrated in Fig. Third, the author reveals a certain relationship between the non-Bloch waves and non-Hermitian topology.
In particular, the classification indicates that an n-th order EP in two dimensions is fully characterized by the braid group Bn, with its . This system is unique because we can create the topological insulating phase from a homogeneous resonator chain only by manipulating gain and loss with a certain order, leading to reconfigurable optical non-trivial topology.
Studies of non-Hermitian effects in quantum condensed matter systems, such as electronic materials, are less common.
Abstract. These phases are characterized by composite cyclic loops of multiple complex-energy bands encircling single or multiple exceptional points (EPs) on the . Non-Hermitian Topology and Exceptional-Point Geometries. Here, the authors report a 2D non-Hermitian . In this chapter, we review topological phases in Hermitian systems and explain non-Hermitian systems. Here, we reveal that, in non-Hermitian systems, robust gapless edge modes can ubiquitously appear owing to a mechanism that is distinct from bulk topology, thus indicating the breakdown of the bulk-edge correspondence. We propose a one-dimensional Floquet ladder that possesses two distinct topological transport channels with opposite directionality. 1 Exceptional non-Hermitian topological edge mode and its application to active matter: Authors: Kazuki Sone*, Yuto Ashida . (12)] form closed loops in a two-dimensional parameter space. Importantly, the non-Hermitian topologicalphenomena havebeen observedex-perimentally in various platforms6-15. The former type of topology exists both for Hermitian and non-Hermitian systems, while the latter is exclusive to non-Hermitian systems, has not been observed yet, and is the focus of the present work. We focus on two-dimensional non-Hermitian systems without any symmetry constraints, which can host two different types of topological point nodes, namely, (i) Fermi points and (ii) exceptional points. The topology of exceptional points is reflected by the phase rigidity scaling exponents. Furthermore, the introduction of non-Hermiticity to topological systems offers a new degree of freedom to control wave propagation, such as concurrent existence of exceptional point and topological edge states, novel non-Hermiticity-induced topological . Quasi-edge states arise rather generally in systems displaying the non-Hermitian skin effect and can be predicted from the non-trivial topology of the energy spectrum under periodic boundary conditions via a bulk-edge correspondence. dI = 0 (dashed) [cf. Knot topology of exceptional point and non-Hermitian no-go theorem Haiping Hu, Shikang Sun, and . which determines the topology in the non-Hermitian case . Abstract: In the band theory for non-Hermitian systems, the energy eigenvalues, which are complex, can exhibit non-trivial topology which is not present in Hermitian systems. The band degeneracy, either the exceptional point of a non-Hermitian system or the Dirac point associated with a topological system, can feature distinct symmetry and topology. Here, we reveal that, in non-Hermitian systems, robust gapless edge modes can ubiquitously appear owing to a mechanism that is distinct from bulk topology, thus indicating the breakdown of the bulk-edge correspondence. I will illustrate this physics through a concrete example: a honeycomb ferromagnet with Dzyaloshinskii-Moriya exchange, comparing interacting spin-wave calculations with an effective non-Hermitian model. It offers a powerful tool in the characterization of both the intrinsic degrees of freedom (DOFs) of a system and the interactions with the external environment.
. 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 this paper, we provide a topological classification of isolated EPs based on homotopy theory. Thus, a natural question to ask is whether the finite non-Hermitian many-particle system has obvious topological properties. Abstract. EJ Bergholtz, JC Budich, FK Kunst. neer non-Hermitian systems in diverse classical and quan- tum settings, ranging from photonics [ 7 - 10 ], phonon- ics [ 11 - 13 ], and optomechanics [ 14 ] to electronics [ 15 ] Understanding the topological properties of non-Hermitian systems has also been the focus of many research efforts [55-59]. Based on the concrete form of the Berry connection, we demonstrate that the exceptional line (EL), at which the eigenstates coalesce, can act as a vortex filament. Most of the existing studies on the topology of non-Hermitian Hamiltonians con- The authors formulate a homotopy classification and knot theory of exceptional points and present a non-Hermitian no-go theorem governing the possible configurations of exceptional points and their splitting rules on a two-dimensional lattice.
The robustness of these edge modes originates from yet another topological structure accompanying the branchpoint singularity . although the conventional notion of topological materials is based on hermitian hamiltonians, effective hamiltonians can become non-hermitian in nonconservative systems including both quantum and. "Our emulator is quite versatile in terms of the possibility of actually monitoring and digging into the dynamics of non-Hermitian systems . These boundary modes, also called skin modes, look quite similar to the boundary states in a topologically non-trivial insulator. 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 this study, we give methods to theoretically detect skin effects and exceptional points by generalizing inversion symmetry. We show that in a generic, ergodic quantum many-body system the interactions induce a nontrivial topology for an arbitrarily small non-Hermitian component of the Hamiltonian. Next, we review the brief history of non-Hermitian . Reviews of Modern Physics 93 (1), 015005, 2021.
These 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. The team found that the topology of an energy surface in a non-Hermitian arrangement plays more of a role in how light behaves in a time evolving system than strict winding around an exceptional . Here, we reveal that, in non-Hermitian systems, robust gapless edge modes can ubiquitously appear owing to a mechanism that is distinct from bulk topology, thus indicating the breakdown of the bulk-edge correspondence. "Exceptional topology of non-Hermitian systems" 24. Exceptional points (EPs) are spectral degeneracies that emerge in open dynamical systems.
topological band theory in Hermitian systems. This system is unique because we can create the topological insulating phase from a homogeneous resonator chain only by manipulating gain and loss with a certain order, leading to reconfigurable optical non-trivial topology. The direction of the EL can be identified by the corresponding Berry .
Among them, a unique feature emerges, known as the non-Hermitian skin effect. The study of Non-Hermitian systems have gained an immense attention and importance in the recent times when it entered the area of topological systems 6,14,15,16 but the criticality in non . This paper shows that non-hermitian quantum many-body systems, constructed as an ``analytic continuation'' of ergodic Hermitian systems, feature an exponential proliferation of exceptional points. . We revisit the problem of classifying topological band structures in non-Hermitian systems.
loss mechanisms, there is an eminent need to reexamine topology within the context of non-Hermitian theories that describe open, lossy systems. Exceptional points (EPs) are peculiar band singularities and play a vital role in a rich array of unusual optical phenomena and non-Hermitian band theory. Gaining topology from loss: Losses can induce nontrivial topology, turning a conventional material into a topological one. 7-9. For the finite non-Hermitian many-particle systems, however, few studies have been done on the topological properties of EP.
"This is the first direct measurement of a non-Hermitian topological invariant associated with an exceptional point in momentum space of a condensed matter system," says Dr Rui Su (Nanyang . Masaya Notomi and Kenta Takata "Non-Hermitian topology and exceptional points in coupled nanoresonators", Proc. Exceptional Topology of Non-Hermitian Systems.
In this paper, we provide a topological classification of isolated EPs based on homotopy theory. Abstract: We review 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. 1 Introduction. Among the exotic phenomena observed in non-Hermitian materials, bulk Fermi arcs [7] hold a special place. February 24, 2021. Knot topology of exceptional point and non-Hermitian no-go theorem Haiping Hu, Shikang Sun, and . However, simple Hamiltonians without band . FK Kunst, V Dwivedi. However, the selective excitation of the system in one among the infinitely many topological quasi-edge states .
Next, we review the brief history of non-Hermitian . one-dimensional non-Hermitian systems with both sublattice symmetry and time-reversal symmetry such as the non-Hermitian Su-Schrieffer-Heeger model, a topological semimetal phase with exceptional points is stabilized by the unique features of the GBZ. The inclusion of non-Hermitian features in topological insulators has recently seen an explosion of activity. The multipartite non-Hermitian Su-Schrieffer-Heeger model is explored as a prototypical example of one-dimensional systems with several sublattice sites for unveiling intriguing insulating and metallic phases with no Hermitian counterparts. Partially because ofthis, the quantum geometry the eigenstates has not been studied extensively in such strongly non-Hermitian systems. Together with the fact that an ideal Hermitian system is usually difficult to realize in real life, the non-Hermitian physics has become a vibrant field in the past few years [17-24].
This is due to an exponential-in-system-size proliferation of exceptional points which have the Hermitian limit as an accumulation (hyper)surface.
. . We propose an anti-parity-time (anti-$\\mathcal{PT}$) symmetric non-Hermitian Su-Schrieffer-Heeger (SSH) model, where the large non-Hermiticity constructively creates nontrivial topology and greatly expands the topological phase. Their synergy will.
The authors formulate a homotopy classification and knot theory of exceptional points and present a non-Hermitian no-go theorem governing the possible configurations of exceptional points and their splitting rules on a two-dimensional lattice. Februar 2021 Publication 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. It describes the phenomenon where an extensive number of boundary modes appears under the open boundary conditions in a non-Hermitian system. The generalization of the Chern number to non-Hermitian Hamiltonians initiated this reexamination; however, there is no established connection between a non-Hermitian topological Then we review topological classifications in terms of the ten-fold Altland-Zirnbauer symmetry class. Non-Hermitian topology in evolutionary game theory: Exceptional points and skin effects in rock-paper-scissors cycles Tsuneya Yoshida, Tomonari Mizoguchi, Yasuhiro Hatsugai Submitted on 2021-09-22. Their topological structures called point-gap topology3-5 are unique to non-Hermitian systems. Band structure in the lossless (real-valued) and lossy (left, real part; right, imaginary part) cases. [] For dissipative systems, the associated eigenspectra are functions of the dissipation rates and an EP occurs at a critical dissipation rate c $\Gamma _c$ around which the real and imaginary part of two or more eigenvalues coalesce and bifurcate, respectively. In particular, we elucidate how the paramount and genuinely NH concept of exceptional degeneracies, at which both .
Their synergy will further produce more exotic topological effects in synthetic matter. 10 (QGT), which includes the Berry curvature (the cornerstone of Hermi- 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. Initial interest revolved around exceptional points exhibiting unique topological features with no counterparts in Hermitian systems, such as Weyl exceptional rings [60], bulk Fermi arcs The generalization of inversion symmetry is unique to non-Hermitian systems. The transport channels occur due to a Z 2 non-Hermitian Floquet topological phase that is protected by time-reversal symmetry. Non-Hermitian skin effects and exceptional points are topological phenomena characterized by integer winding numbers. Special attentions are given to exceptional points - branch-point singularities on the complex eigenvalue manifolds that exhibit non-trivial topological properties.
Namely, under a change of a system parameter, the GBZ is deformed so that The search for topological states in non-Hermitian systems, and more specifically in non-Hermitian lattice models, has become a newly emerging research front.Non-Hermitian systems are much more than a theoretical curiosity, they arise naturally in the description of the finite lifetime due to interactions, or more prominently, in photonic or acoustic systems. 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. 1a). In particular, how the paramount and genuinely NH concept of exceptional degeneracies, at which both eigenvalues and eigenvectors . Mapping between Non-Hermitian Quantum and Classical Models The non-Hermitian topology contained in the model of Eq. Abstract. Schematic diagram of the proposed non-Hermitian system based on coupled Fabry-Prot microcavities is illustrated in Fig. Third, the author reveals a certain relationship between the non-Bloch waves and non-Hermitian topology.
In particular, the classification indicates that an n-th order EP in two dimensions is fully characterized by the braid group Bn, with its . This system is unique because we can create the topological insulating phase from a homogeneous resonator chain only by manipulating gain and loss with a certain order, leading to reconfigurable optical non-trivial topology.
Studies of non-Hermitian effects in quantum condensed matter systems, such as electronic materials, are less common.
Abstract. These phases are characterized by composite cyclic loops of multiple complex-energy bands encircling single or multiple exceptional points (EPs) on the . Non-Hermitian Topology and Exceptional-Point Geometries. Here, the authors report a 2D non-Hermitian . In this chapter, we review topological phases in Hermitian systems and explain non-Hermitian systems. Here, we reveal that, in non-Hermitian systems, robust gapless edge modes can ubiquitously appear owing to a mechanism that is distinct from bulk topology, thus indicating the breakdown of the bulk-edge correspondence. We propose a one-dimensional Floquet ladder that possesses two distinct topological transport channels with opposite directionality. 1 Exceptional non-Hermitian topological edge mode and its application to active matter: Authors: Kazuki Sone*, Yuto Ashida . (12)] form closed loops in a two-dimensional parameter space. Importantly, the non-Hermitian topologicalphenomena havebeen observedex-perimentally in various platforms6-15. The former type of topology exists both for Hermitian and non-Hermitian systems, while the latter is exclusive to non-Hermitian systems, has not been observed yet, and is the focus of the present work. We focus on two-dimensional non-Hermitian systems without any symmetry constraints, which can host two different types of topological point nodes, namely, (i) Fermi points and (ii) exceptional points. The topology of exceptional points is reflected by the phase rigidity scaling exponents. Furthermore, the introduction of non-Hermiticity to topological systems offers a new degree of freedom to control wave propagation, such as concurrent existence of exceptional point and topological edge states, novel non-Hermiticity-induced topological . Quasi-edge states arise rather generally in systems displaying the non-Hermitian skin effect and can be predicted from the non-trivial topology of the energy spectrum under periodic boundary conditions via a bulk-edge correspondence. dI = 0 (dashed) [cf. Knot topology of exceptional point and non-Hermitian no-go theorem Haiping Hu, Shikang Sun, and . which determines the topology in the non-Hermitian case . Abstract: In the band theory for non-Hermitian systems, the energy eigenvalues, which are complex, can exhibit non-trivial topology which is not present in Hermitian systems. The band degeneracy, either the exceptional point of a non-Hermitian system or the Dirac point associated with a topological system, can feature distinct symmetry and topology. Here, we reveal that, in non-Hermitian systems, robust gapless edge modes can ubiquitously appear owing to a mechanism that is distinct from bulk topology, thus indicating the breakdown of the bulk-edge correspondence. I will illustrate this physics through a concrete example: a honeycomb ferromagnet with Dzyaloshinskii-Moriya exchange, comparing interacting spin-wave calculations with an effective non-Hermitian model. It offers a powerful tool in the characterization of both the intrinsic degrees of freedom (DOFs) of a system and the interactions with the external environment.
. 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 this paper, we provide a topological classification of isolated EPs based on homotopy theory. Thus, a natural question to ask is whether the finite non-Hermitian many-particle system has obvious topological properties. Abstract. EJ Bergholtz, JC Budich, FK Kunst. neer non-Hermitian systems in diverse classical and quan- tum settings, ranging from photonics [ 7 - 10 ], phonon- ics [ 11 - 13 ], and optomechanics [ 14 ] to electronics [ 15 ] Understanding the topological properties of non-Hermitian systems has also been the focus of many research efforts [55-59]. Based on the concrete form of the Berry connection, we demonstrate that the exceptional line (EL), at which the eigenstates coalesce, can act as a vortex filament. Most of the existing studies on the topology of non-Hermitian Hamiltonians con- The authors formulate a homotopy classification and knot theory of exceptional points and present a non-Hermitian no-go theorem governing the possible configurations of exceptional points and their splitting rules on a two-dimensional lattice.
The robustness of these edge modes originates from yet another topological structure accompanying the branchpoint singularity . although the conventional notion of topological materials is based on hermitian hamiltonians, effective hamiltonians can become non-hermitian in nonconservative systems including both quantum and. "Our emulator is quite versatile in terms of the possibility of actually monitoring and digging into the dynamics of non-Hermitian systems . These boundary modes, also called skin modes, look quite similar to the boundary states in a topologically non-trivial insulator. 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 this study, we give methods to theoretically detect skin effects and exceptional points by generalizing inversion symmetry. We show that in a generic, ergodic quantum many-body system the interactions induce a nontrivial topology for an arbitrarily small non-Hermitian component of the Hamiltonian. Next, we review the brief history of non-Hermitian . Reviews of Modern Physics 93 (1), 015005, 2021.
These 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. The team found that the topology of an energy surface in a non-Hermitian arrangement plays more of a role in how light behaves in a time evolving system than strict winding around an exceptional . Here, we reveal that, in non-Hermitian systems, robust gapless edge modes can ubiquitously appear owing to a mechanism that is distinct from bulk topology, thus indicating the breakdown of the bulk-edge correspondence. "Exceptional topology of non-Hermitian systems" 24. Exceptional points (EPs) are spectral degeneracies that emerge in open dynamical systems.
topological band theory in Hermitian systems. This system is unique because we can create the topological insulating phase from a homogeneous resonator chain only by manipulating gain and loss with a certain order, leading to reconfigurable optical non-trivial topology. The direction of the EL can be identified by the corresponding Berry .
Among them, a unique feature emerges, known as the non-Hermitian skin effect. The study of Non-Hermitian systems have gained an immense attention and importance in the recent times when it entered the area of topological systems 6,14,15,16 but the criticality in non . This paper shows that non-hermitian quantum many-body systems, constructed as an ``analytic continuation'' of ergodic Hermitian systems, feature an exponential proliferation of exceptional points. . We revisit the problem of classifying topological band structures in non-Hermitian systems.
loss mechanisms, there is an eminent need to reexamine topology within the context of non-Hermitian theories that describe open, lossy systems. Exceptional points (EPs) are peculiar band singularities and play a vital role in a rich array of unusual optical phenomena and non-Hermitian band theory. Gaining topology from loss: Losses can induce nontrivial topology, turning a conventional material into a topological one. 7-9. For the finite non-Hermitian many-particle systems, however, few studies have been done on the topological properties of EP.
"This is the first direct measurement of a non-Hermitian topological invariant associated with an exceptional point in momentum space of a condensed matter system," says Dr Rui Su (Nanyang . Masaya Notomi and Kenta Takata "Non-Hermitian topology and exceptional points in coupled nanoresonators", Proc. Exceptional Topology of Non-Hermitian Systems.
In this paper, we provide a topological classification of isolated EPs based on homotopy theory. Abstract: We review 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. 1 Introduction. Among the exotic phenomena observed in non-Hermitian materials, bulk Fermi arcs [7] hold a special place. February 24, 2021. Knot topology of exceptional point and non-Hermitian no-go theorem Haiping Hu, Shikang Sun, and . However, simple Hamiltonians without band . FK Kunst, V Dwivedi. However, the selective excitation of the system in one among the infinitely many topological quasi-edge states .
Next, we review the brief history of non-Hermitian . one-dimensional non-Hermitian systems with both sublattice symmetry and time-reversal symmetry such as the non-Hermitian Su-Schrieffer-Heeger model, a topological semimetal phase with exceptional points is stabilized by the unique features of the GBZ. The inclusion of non-Hermitian features in topological insulators has recently seen an explosion of activity. The multipartite non-Hermitian Su-Schrieffer-Heeger model is explored as a prototypical example of one-dimensional systems with several sublattice sites for unveiling intriguing insulating and metallic phases with no Hermitian counterparts. Partially because ofthis, the quantum geometry the eigenstates has not been studied extensively in such strongly non-Hermitian systems. Together with the fact that an ideal Hermitian system is usually difficult to realize in real life, the non-Hermitian physics has become a vibrant field in the past few years [17-24].
This is due to an exponential-in-system-size proliferation of exceptional points which have the Hermitian limit as an accumulation (hyper)surface.