Related papers: Green's functions of multiband non-Hermitian syste…
Although the non-Bloch band theory is a milestone in elaborating bulk energy bands of non-Hermitian systems under the open-boundary condition (OBC), vital issues related to multivalued functions of non-Hermitian energy bands remain…
Green's functions are fundamental quantities that determine the linear responses of physical systems. The recent developments of non-Hermitian systems, therefore, call for Green's function formulas of non-Hermitian bands. This task is…
Green's function in non-Hermitian systems has recently been revealed to be capable of directional amplification in some cases. The exact formulas for end-to-end Green's functions are significantly important for studies of both non-Hermitian…
We consider conditions for the existence of boundary modes in non-Hermitian systems with edges of arbitrary co-dimension. Through a universal formulation of formation criteria for boundary modes in terms of local Green functions, we outline…
A nonzero non-Hermitian winding number indicates that a gapped system is in a nontrivial topological class due to the non-Hermiticity of its Hamiltonian. While for Hermitian systems nontrivial topological quantum numbers are reflected by…
In non-Hermitian systems, it is a counterintuitive feature of the non-Hermitian skin effect (NHSE) that the energy spectrum and eigenstates can be totally different under open or periodic boundary conditions, suggesting that non-Hermitian…
Periodic-boundary spectrum, open-boundary spectrum, as well as the generalized Brillouin zone (GBZ) are three essential properties of a one-dimensional non-Hermitian system. In this paper we illustrate that the deep connections between them…
In this paper, we employ the generalized Bloch theory to rediscover the generalized Brillouin zone theory and follow this way to obtain the Green's function of the non-Hermitian system. We focus on a classical chiral model and give the…
Non-Hermitian skin effect, namely that the eigenvalues and eigenstates of a non-Hermitian tight-binding Hamiltonian have significant differences under open or periodic boundary conditions, is a remarkable phenomenon of non-Hermitian…
We study the Green's functions in non-Hermitian systems exhibiting the critical non-Hermitian skin effect (critical NHSE) using a double-chain Hatano-Nelson model with inter-chain coupling $\Delta$. For $\Delta=0$, the system decouples into…
We provide a systematic and self-consistent method to calculate the generalized Brillouin Zone (GBZ) analytically in one dimensional non-Hermitian systems, which helps us to understand the non-Hermitian bulk-boundary correspondence. In…
Genuinely non-Hermitian topological phases can be realized in open systems with sufficiently strong gain and loss; in such phases, the Hamiltonian cannot be deformed into a gapped Hermitian Hamiltonian without energy bands touching each…
Complex-valued physical quantities, often non-conserved, represent key phenomena in non-Hermitian systems such as dissipation and localization. Recent advancements in non-Hermitian physics have revealed boundary-condition-sensitive band…
A striking feature of non-Hermitian tight-binding Hamiltonians is the high sensitivity of both spectrum and eigenstates to boundary conditions. Indeed, if the spectrum under periodic boundary conditions is point gapped, by opening the…
In this work, we demonstrate the presence of an anomalous non-Hermitian skin effects which decay from both ends of a system consisting of two coupled Hermitian chains induced by non-reciprocal inter-chain cross-coupling. Another intriguing…
In recent research, it has been shown that non-Hermitian systems exhibit sensitivity to boundaries, and it is caused by the non-Hermitian skin effect. In this work, we construct the non-Bloch band theory in bosonic Bogoliubov--de Gennes…
One of the most pronounced non-Hermitian phenomena is the non-Hermitian skin effect, which refers to the exponential localization of bulk eigenstates near the boundaries of non-Hermitian systems. Whereas non-Bloch band theory has been…
In spatially periodic Hermitian systems, such as electronic systems in crystals, the band structure is described by the band theory in terms of the Bloch wave functions, which reproduce energy levels for large systems with open boundaries.…
In this work, we propose a theory on the two-dimensional non-Hermitian skin effect by resolving two representative minimal models. Specifically, we show that for any given non-Hermitian Hamiltonian, (i) the corresponding region covered by…
We review some recent techniques for dealing with non-hermitian random matrix models based on generalized Green's functions. We introduce the diagrammatic methods in the hermitian case and generalize them to the non-hermitian case. The…