Related papers: Bulk-boundary correspondence in topological two-di…
The non-Hermitian skin effect (NHSE) fundamentally invalidates the conventional bulk-boundary correspondence (BBC), leading topological diagnostics into a crisis. While the non-Bloch polarization $P_{\beta}$ defined on the generalized…
Non-Hermitian topological systems show quite different properties as their Hermitian counterparts. An important, puzzled issue on non-Hermitian topological systems is the existence of defective edge states beyond usual bulk-boundary…
Non-Hermitian skin-edge states emerge only at one edge in one-dimensional nonreciprocal chains, where all states are localized at the edge irrespective of eigenvalues. The bulk topological number is the winding number associated with the…
The bulk-edge correspondence (BEC) is the hallmark of topological systems. In continuous (nonlattice) Hermitian systems with an unbounded wave vector, it was recently shown that the BEC of Chern insulators is modified. How would it be…
We consider Toeplitz operators defined on a concave corner-shaped subset of the square lattice. We obtain a necessary and sufficient condition for these operators to be Fredholm. We further construct a Fredholm concave corner Toeplitz…
Topological theory predicts the necessary conditions for robust dimensional reduction in a host of quantum and classical systems. Models have recently been proposed for stochastic systems which describe many biological and chemical…
We identify quantum geometric bounds for observables in non-Hermitian systems. We find unique bounds on non-Hermitian quantum geometric tensors, generalized two-point response correlators, conductivity tensors, and optical weights. We…
We develop a theory of edge states based on the Hermiticity of Hamiltonian operators for tight-binding models defined on lattices with boundaries. We describe Hamiltonians using shift operators which serve as differential operators in…
Topological stability of the edge states is investigated for non-Hermitian systems. We examine two classes of non-Hermitian Hamiltonians supporting real bulk eigenenergies in weak non-Hermiticity: SU(1,1) and SO(3,2) Hamiltonians. As an…
The discovery of topological phases has ushered in a new era of condensed matter physics and revealed a variety of natural and artificial materials. They obey the bulk-boundary correspondence (BBC), which guarantees the emergence of…
In Hermitian topological systems, the bulk-boundary correspondence strictly constraints boundary transport to values determined by the topological properties of the bulk. We demonstrate that this constraint can be lifted in non-Hermitian…
A scenario of non-Hermitian bulk--boundary correspondence proposed for one-dimensional topological insulators is adapted to a non-Hermitian Chern insulator to examine its applicability to two-dimensional systems. This scenario employs bulk…
Light can mediate effective dipole-dipole interactions between atoms or quantum emitters coupled to a common environment. Exploiting them to tailor a desired effective Hamiltonian can have major applications and advance the search for…
Non-Hermitian band theory distinguishes between line gaps and point gaps. While point gaps can give rise to intrinsic non-Hermitian band topology without Hermitian counterparts, line-gapped systems can always be adiabatically deformed to a…
Topological semimetals exhibit protected band crossings in momentum space, accompanied by corresponding surface states. Non-Hermitian Hamiltonians introduce geometry-sensitive features that dissolve this bulk-boundary correspondence…
We analyze chiral topological edge modes in a non-Hermitian variant of the 2D Dirac equation. Such modes appear at interfaces between media with different "masses" and/or signs of the "non-Hermitian charge". The existence of these edge…
We identify and investigate two classes of non-Hermitian systems, i.e., one resulting from Lorentz-symmetry violation (LSV) and the other from a complex mass (CM) with Lorentz invariance, from the perspective of quantum field theory. The…
We develop the topological band theory for systems described by non-Hermitian Hamiltonians, whose energy spectra are generally complex. After generalizing the notion of gapped band structures to the non-Hermitian case, we classify "gapped"…
Recently, the search for topological states of matter has turned to non-Hermitian systems, which exhibit a rich variety of unique properties without Hermitian counterparts. Lattices modeled through non-Hermitian Hamiltonians appear in the…
The bulk-boundary correspondence relates topologically-protected edge modes to bulk topological invariants, and is well-understood for short-range free-fermion chains. Although case studies have considered long-range Hamiltonians whose…