Related papers: Recurrence method in Non-Hermitian Systems
We develop a systematically general theory of one-dimensional (1D) non-Hermitian systems, elaborating on the energy bands, the band degeneracy, and the defectiveness of eigenstates under open boundary conditions. We analyze the band…
In recent years, non-Hermitian phases in classical and quantum systems have garnered significant attention. In particular, their intriguing band geometry offers a platform for exploring unique topological states and unconventional quantum…
The complex eigenenergies and non-orthogonal eigenstates of non-Hermitian systems exhibit unique topological phenomena that cannot appear in Hermitian systems. Representative examples are the non-Hermitian skin effect and exceptional…
Dramatically different from the Hermitian systems, the conventional Bulk-Boundary Correspondence (BBC) is broken in the non-Hermitian systems. In this article, we use edge entanglement entropy to characterize the topological properties of…
The non-trivial topological features in the energy band of non-Hermitian systems provide promising pathways to achieve robust physical behaviors in classical or quantum open systems. A key topological feature, unique to non-Hermitian…
In contrast to eigenvalue-based approaches, we formulate the bulk-boundary correspondence for two-dimensional non-Hermitian quadratic lattice Hamiltonians in terms of Toeplitz operators and singular values, which correctly capture the…
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…
We propose a Hermite spectral method for the inelastic Boltzmann equation, which makes two-dimensional periodic problem computation affordable by the hardware nowadays. The new algorithm is based on a Hermite expansion, where the expansion…
We present a pedagogical review of the periodically driven non-Hermitian systems, particularly on the rich interplay between the non-Hermitian skin effect and the topology. We start by reviewing the non-Bloch band theory of the static…
Non-Hermitian systems play a central role in nonequilibrium physics, where determining the energy spectrum under open boundary conditions is a fundamental problem. Non-Bloch band theory, based on the characteristic equation $\text{det}[E -…
We establish non-Hermitian topological mechanics in one dimensional (1D) and two dimensional (2D) lattices consisting of mass points connected by meta-beams that lead to odd elasticity. Extended from the "non-Hermitian skin effect" in 1D…
The localization is one of the active and fundamental research in topology physics. Based on a generalized Su-Schrieffer-Heeger model with the quasiperiodic non-Hermitian emerging at the off-diagonal location, we propose a novel systematic…
Non-Hermiticity naturally arises in many physical systems that exchange energy with their environment. The presence of non-Hermiticity leads to many novel topological physics phenomena and device applications. In the non-Hermitian energy…
The bulk-boundary or bulk-edge correspondence is a principle relating surface confined states to the topological classification of the bulk. By combining non-Hermitian ingredients in terms of gain or loss with media that violate…
There has been much recent interest and progress on topological structures of the non-Hermitian Bloch bands. Here, we study the topological structures of non-Bloch bands of non-Hermitian multiband quantum systems under open boundary…
A striking feature of non-Hermitian systems is the presence of two different types of topology. One generalizes Hermitian topological phases, and the other is intrinsic to non-Hermitian systems, which are called line-gap topology and…
Symmetry of non-Hermitian matrices underpins many physical phenomena. In particular, chaotic open quantum systems exhibit universal bulk spectral correlations classified on the basis of time-reversal symmetry$^{\dagger}$ (TRS$^{\dagger}$),…
We examine a non-Hermitian (NH) tight-binding system comprising of two orbitals per unit cell and their electrical circuit analogues. We distinguish the PT-symmetric and non-PT symmetric cases characterised by non-reciprocal nearest…
We show that the bulk-boundary correspondence for topological insulators can be modified in the presence of non-Hermiticity. We consider a one-dimensional tight-binding model with gain and loss as well as long-range hopping. The system is…
A set of Hamiltonians that are not self-adjoint but have the spectrum of the harmonic oscillator is studied. The eigenvectors of these operators and those of their Hermitian conjugates form a bi-orthogonal system that provides a…