相关论文: Graph Morphology of Non-Hermitian Bands

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.…

The non-Bloch band theory can describe energy bands in a one-dimensional (1D) non-Hermitian system. On the other hand, whether the non-Bloch band theory can be extended to higher-dimensional non-Hermitian systems is nontrivial. In this…

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…

In this paper, we review our non-Bloch band theory in one-dimensional non-Hermitian tight-binding systems. In our theory, it is shown that in non-Hermitian systems, the Brillouin zone is determined so as to reproduce continuum energy bands…

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"…

Nonlinear eigenvalue problems arise in a wide range of physical systems, in which system parameters depend on the eigenvalue. Such systems have been proposed to exhibit an extreme sensitivity of their spectra to boundary conditions, which…

The non-Hermitian skin effect, as a unique feature of non-Hermitian systems, will break the topological energy braiding of the Bloch bands in open boundary systems. Going beyond the Bloch band theory, we unveil the energy braiding of the…

Unlike Hermitian systems, non-Hermitian energy spectra under periodic boundary conditions can form closed loops in the complex energy plane, a phenomenon known as point gap topology. In this paper, we investigate the self-intersection…

We uncover the very rich graph topology of generic bounded non-Hermitian spectra, distinct from the topology of conventional band invariants and complex spectral winding. The graph configuration of complex spectra are characterized by the…

Within the expanding field of non-Hermitian physics, non-Hermitian pumping has emerged as a key phenomenon, epitomized through the skin effect via extensive boundary mode accumulation modifying the conventional Bloch picture. Beyond…

The non-Bloch topology leads to the emergence of various counter-intuitive phenomena in non-Hermitian systems under the open boundary condition (OBC), which can not find a counterpart in Hermitian systems. However, in the non-Hermitian…

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 -…

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…

We show topological configurations of the complex-valued spectra in gapped non-Hermitian systems. These arise when the distinctive EPs in the energy Riemann sheets of such models are annihilated after threading them across the boundary of…

Real-valued band structures are foundational to analyzing periodic systems within the Hermitian description and have been experimentally well-established over recent decades. In contrast, non-Hermitian systems exhibit complex band…

We formulate quantum geometry for non-Hermitian systems under open boundary conditions. By defining quantum-geometric quantities in both real-space and non-Bloch representations, we establish a unified framework beyond conventional Bloch…

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 two- and higher-dimensional non-Hermitian lattices, systems can exhibit geometry-dependent bands, where the spectrum and eigenstates under open boundary conditions depend on the bulk geometry even in the thermodynamic limit. Although…

The topology of non-Hermitian systems is drastically shaped by the non-Hermitian skin effect, which leads to the generalized bulk-boundary correspondence and non-Bloch band theory. The essential part in formulations of bulk-boundary…

The hyperbolic lattice (HBL) has emerged as a compelling platform for exploring matter in non-Euclidean space. Among its notable features, the breakdown of the conventional Bloch theorem stands out, prompting a reexamination of band theory,…