Quantum systems that are coupled to an external bath can often be described in terms of a non-Hermitian effective Hamiltonian. In isolated with Hermitian Hamiltonians, topological aspects the band structure, and resulting phases, have been interest. The combination two concepts, i.e., properties open systems, leads qualitatively new effects. This review provides introduction these quantum mechanical concepts their classical analogs, discusses number applications ranging from metamaterials...

Non-Hermitian systems exhibit striking exceptions from the paradigmatic bulk-boundary correspondence, including failure of bulk Bloch band invariants in predicting boundary states and (dis)appearance at parameter values far those corresponding to gap closings periodic without boundaries. Here, we provide a comprehensive framework unravel this disparity based on notion biorthogonal quantum mechanics: While properties left right eigenstates modes are individually decoupled physics...

Non-Hermitian Hamiltonians, which describe a wide range of dissipative systems, and higher-order topological phases, exhibit novel boundary states on corners hinges, comprise two areas intense current research. Here we investigate systems where these frontiers merge formulate generalized biorthogonal bulk-boundary correspondence, dictates the appearance modes at parameter values that are, in general, radically different from those mark phase transitions periodic systems. By analyzing...

Symmetry plays a paramount role for the classification of phases matter occurring in nature. Combining symmetry analysis with concepts from topology that allow us to identify global and robust physical properties, new quantum matter, such as topological insulators semimetals, have been discovered recent years. Here, authors analyze general exemplify importance symmetries dissipative counterparts semimetals non-Hermitian systems, thus introducing notion symmetry-protected nodal phases.

Topological phases of Hermitian systems are known to exhibit intriguing properties such as the presence robust boundary states and famed bulk-boundary correspondence. These features can change drastically for their non-Hermitian generalizations, exemplified by a general breakdown correspondence localization all at boundary, termed skin effect. In this article, we present completely analytical unifying framework studying these using generalized transfer matrices -- real-space approach...

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 structure as such does not depend fine tuning, allowing us to track their evolution throughout various phases across phase transitions. Most saliently, our provide ``boundary solvable'' examples of recently introduced higher-order topological phases. apply...

Exceptional points (EPs) appear as degeneracies in the spectrum of non-Hermitian matrices at which eigenvectors coalesce. In general, an EP order $n$ may find room to emerge if $2(n\ensuremath{-}1)$ real constraints are imposed. Our results show that these can be expressed terms determinant and traces matrix. findings further reveal total number reduce presence unitary antiunitary symmetries. Additionally, we draw generic conclusions for asymptotic dispersion EPs. Based on our calculations,...

One of the unique features non-Hermitian (NH) systems is appearance NH degeneracies known as exceptional points (EPs). The extensively studied defective EPs occur when Hamiltonian becomes non-diagonalizable. Aside from this degeneracy, we show that may host two further types non-defective degeneracies, namely, and ordinary (Hermitian) nodal points. manifest themselves by i) diagonalizability at these ii) non-diagonalizability along certain intersections points, resulting in instabilities...

Both non-Hermitian systems and the behaviour of emitters coupled to structured baths have been studied intensely in recent years. Here we study interplay these paradigmatic settings. In a series examples, show that single quantum emitter bath displays number unconventional behaviours, many without Hermitian counterpart. We first consider unidirectional hopping lattice whose complex dispersion forms loop. identify peculiar bound states inside loop as manifestation skin effect. same setting,...

The hallmark of topological phases is their robust boundary signature whose intriguing properties---such as the one-way transport on chiral edge a Chern insulator and sudden disappearance surface states forming open Fermi arcs surfaces Weyl semimetals---are impossible to realize alone. Yet, despite glaring simplicity noninteracting bulk Hamiltonians concomitant energy spectrum, detailed study corresponding has essentially been restricted numerical simulation. In this work, however, we show...

We establish a general framework for studying the bound states and photon-emission dynamics of quantum emitters coupled to structured nanophotonic lattices with engineered dissipation (loss). In single-excitation sector, system can be described exactly by non-Hermitian formalism. have pointed out in accompanying letter [Gong et al., Phys. Rev. Lett. 129, 223601 (2022)] that single emitter one-dimensional lattice may already exhibit anomalous behaviors without Hermitian counterparts. Here we...

Nonlinearity and non-Hermiticity, for example due to environmental gain-loss processes, are a common occurrence throughout numerous areas of science lie at the root many remarkable phenomena. For latter, parity-time-reflection (<a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mi mathvariant="script">PT</a:mi></a:math>) symmetry has played an eminent role in understanding exceptional-point structures phase transitions these systems. Yet their interplay remained, by large, unexplored....

While the Bloch spectrum of translationally invariant noninteracting lattice models is trivially obtained by a Fourier transformation, diagonalizing same problem in presence open boundary conditions typically only possible numerically or idealized limits. Here we present exact analytic solutions for states number current interest, including nodal-line semimetals on hyperhoneycomb lattice, spin-orbit coupled graphene, and three-dimensional topological insulators diamond which no previous...

Four-dimensional quantum Hall (QH) models usually rely on synthetic dimensions for their simulation in experiment. Here, we study a QH system which features nontrivial configuration of three-dimensional Weyl cones its boundaries. We propose analog this model the form dissipative semimetal (WSM) described by non-Hermitian (NH) Hamiltonian, long-time limit manifests anomalous boundary physics four-dimensional bulk spectrum. The topology NH WSM is captured winding number whose value directly...

Abstract The spectral properties of a non‐Hermitian quasi‐1D lattice in two the possible dimerization configurations are investigated. Specifically, it focuses on diamond chain that presents zero‐energy flat band. band originates from wave interference and results eigenstates with finite contribution only sites unit cell. To achieve characteristics, system under study non‐reciprocal hopping terms chain. This leads to accumulation boundary system, known as skin effect. Despite this...

Exceptional points of order <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mi>n</a:mi></a:math> <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mrow><b:mo>(</b:mo><b:mi>EP</b:mi><b:mi>n</b:mi><b:mi mathvariant="normal">s</b:mi><b:mo>)</b:mo></b:mrow></b:math> appear in non-Hermitian systems as where the eigenvalues and eigenvectors coalesce. They emerge if <d:math...

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 surfaces. These represent class of "sweet spots" in the space possible tight-binding models---the exact solutions remain valid any parameters as long they obey simple locality conditions that are manifest underlying structure. Consequently, our capture physics both (higher-order) topological non-topological phases...

Non-Hermitian Hamiltonians, which effectively describe dissipative systems, and analogue gravity models, simulate properties of gravitational objects, comprise seemingly different areas current research. Here, we investigate the interplay between two by relating parity-time-symmetric Weyl-type Hamiltonians to Schwarzschild black holes emitting Hawking radiation. We show that exceptional points these form tilted cones mimicking behavior light cone a radially infalling observer approaching...

Exceptional points (EPs) are truly non-Hermitian (NH) degeneracies where matrices become defective. The order of such an EP is given by the number coalescing eigenvectors. On one hand, most work focusses on studying $N$th-order EPs in $N\leq4$-dimensional NH Bloch Hamiltonians. other some works have remarked existence orders scaling with systems size models exhibiting skin effect. In this letter, we introduce a new type and provide recipe how to realize arbitrary not system size. We...

Non-Hermitian (NH) Hamiltonians can be used to describe dissipative systems, notably including systems with gain and loss, are currently intensively studied in the context of topology. A salient difference between Hermitian NH models is breakdown conventional bulk-boundary correspondence, invalidating use topological invariants computed from Bloch bands characterize boundary modes generic systems. One way overcome this difficulty framework biorthogonal quantum mechanics define a...

We theoretically study the competition between two possible exotic superconducting orders that may occur in graphene-like systems, assuming dominant nearest-neighbor attraction: gapless hidden order, which renormalizes Fermi velocity, and Kekule opens a gap. perform an analysis within mean-field theory for Dirac electrons, at finite temperature chemical potential, as well half filling zero temperature, first excluding possibility of coexistence orders. In case, we find dependence critical...

Magnetotransport experiments on Weyl semimetals are essential for investigating the intriguing topological and low-energy properties of nodes. If transport direction is perpendicular to applied magnetic field, have shown a large positive magnetoresistance. In this work we present theoretical scattering matrix approach transversal magnetotransport in node. Our numerical method confirms goes beyond existing perturbative analytical by treating disorder exactly. It formulated real space...

Exceptional points of order $n$ (EP$n$s) appear in non-Hermitian systems as where the eigenvalues and eigenvectors coalesce. Whereas EP2s generically two dimensions (2D), higher-order EPs require a higher-dimensional parameter space to emerge. In this work, we provide complete characterization appearance symmetry-induced 2D space. We find that besides only EP3s, EP4s, EP5s can be stabilized 2D. Moreover, these must always pairs with their dispersion determined by symmetries. Upon studying...