Non-Hermitian skin effect in arbitrary dimensions: non-Bloch band theory and classification
- URL: http://arxiv.org/abs/2407.01296v1
- Date: Mon, 1 Jul 2024 13:49:53 GMT
- Title: Non-Hermitian skin effect in arbitrary dimensions: non-Bloch band theory and classification
- Authors: Yuncheng Xiong, Ze-Yu Xing, Haiping Hu,
- Abstract summary: Non-Hermitian skin effect (NHSE) is a distinctive phenomenon in non-Hermitian systems.
NHSE is characterized by a significant accumulation of eigenstates at system boundaries.
We present a geometry-adaptive non-Bloch band theory in arbitrary dimensions.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Non-Hermitian skin effect (NHSE) is a distinctive phenomenon in non-Hermitian systems, characterized by a significant accumulation of eigenstates at system boundaries. While well-understood in one dimension via non-Bloch band theory, unraveling the NHSE in higher dimensions faces formidable challenges due to the diversity of open boundary conditions or lattice geometries and inevitable numerical errors. Key issues, including higher-dimensional non-Bloch band theory, geometric dependency, spectral convergence and stability, and a complete classification of NHSE, remain elusive. In this work, we address these challenges by presenting a geometry-adaptive non-Bloch band theory in arbitrary dimensions, through the lens of spectral potential. Our formulation accurately determines the energy spectra, density of states, and generalized Brillouin zone for a given geometry in the thermodynamic limit (TDL), revealing their geometric dependencies. Furthermore, we systematically classify the NHSE into critical and non-reciprocal types using net winding numbers. In the critical case, we identify novel scale-free skin modes residing on the boundary. In the nonreciprocal case, the skin modes manifest in various forms, including normal or anomalous corner modes, boundary modes or scale-free modes. We reveal the non-convergence and instability of the non-Bloch spectra in the presence of scale-free modes and attribute it to the non-exchangeability of the zero-perturbation limit and the TDL. The instability drives the energy spectra towards the Amoeba spectra in the critical case. Our findings provide a unified non-Bloch band theory governing the energy spectra, density of states, and generalized Brillouin zone in the TDL, offering a comprehensive understanding of NHSE in arbitrary dimensions.
Related papers
- Gapless Floquet topology [40.2428948628001]
We study the existence of topological edge zero- and pi-modes despite the lack of bulk gaps in the quasienergy spectrum.
We numerically study the effect of interactions, which give a finite lifetime to the edge modes in the thermodynamic limit with the decay rate consistent with Fermi's Golden Rule.
arXiv Detail & Related papers (2024-11-04T19:05:28Z) - Topological Order in the Spectral Riemann Surfaces of Non-Hermitian Systems [44.99833362998488]
We show topologically ordered states in the complex-valued spectra of non-Hermitian systems.
These arise when the distinctive exceptional points in the energy surfaces of such models are annihilated.
We illustrate the characteristics of the topologically protected states in a non-Hermitian two-band model.
arXiv Detail & Related papers (2024-10-24T10:16:47Z) - Quantum Chaos on Edge [36.136619420474766]
We identify two different classes: the near edge physics of sparse'' and the near edge of dense'' chaotic systems.
The distinction lies in the ratio between the number of a system's random parameters and its Hilbert space dimension.
While the two families share identical spectral correlations at energy scales comparable to the level spacing, the density of states and its fluctuations near the edge are different.
arXiv Detail & Related papers (2024-03-20T11:31:51Z) - Universal scalefree non-Hermitian skin effect near the Bloch point [5.261047057490265]
The scalefree non-Hermitian skin effect (NHSE) refers to the phenomenon that the localization length of skin modes scales proportionally with system size in non-Hermitian systems.
In this paper, we suggest that the scalefree NHSE is a universal phenomenon, observable in extensive systems if these systems can be described by non-Bloch band theory.
arXiv Detail & Related papers (2023-11-24T06:24:50Z) - Non-Bloch band theory for non-Hermitian continuum systems [1.2845309023495566]
We generalize the non-Bloch band theory to non-Hermitian continuum systems.
We show that the appropriate discretization of continuum systems into lattice models requires matching the hopping range of the latter to the number of boundary conditions.
Our theory serves as a useful toolbox for investigating the rich non-Bloch physics in non-Hermitian continuum systems.
arXiv Detail & Related papers (2023-10-12T17:57:24Z) - Geometry-dependent skin effect and anisotropic Bloch oscillations in a
non-Hermitian optical lattice [5.593595192885069]
geometry-dependent skin effect (GDSE) refers to that the localization of extensive eigenstates depends on the system's geometry under open boundary conditions.
In this paper, we demonstrate the emergence of GDSE in a two-dimensional $sp$ optical ladder lattice with on-site atom loss.
Our results reveal that the GDSE has an intrinsic anisotropic bulk dynamics independent of boundary conditions, and offer its realization and detection in quantum systems.
arXiv Detail & Related papers (2023-04-07T18:00:07Z) - Amoeba Formulation of Non-Bloch Band Theory in Arbitrary Dimensions [9.924017206241272]
We develop a formulation of the non-Hermitian skin effect and non-Bloch band theory in arbitrary spatial dimensions.
Key quantities of non-Hermitian bands, including the energy spectrum, eigenstates profiles, and the generalized Brillouin zone, can be efficiently obtained from this approach.
arXiv Detail & Related papers (2022-12-22T14:34:51Z) - A Theorem on Extensive Spectral Degeneracy for Systems with Higher
Symmetries in General Dimensions [0.0]
We establish lower bounds on the spectral degeneracy of quantum systems with higher Gauge Like symmetries.
We exploit the effects of modified boundary conditions.
We briefly discuss why, in spite of the proven large degeneracy associated with infrared-ultraviolet mixing, some systems may still exhibit conventional physical behaviors.
arXiv Detail & Related papers (2022-08-24T17:50:52Z) - Role of boundary conditions in the full counting statistics of
topological defects after crossing a continuous phase transition [62.997667081978825]
We analyze the role of boundary conditions in the statistics of topological defects.
We show that for fast and moderate quenches, the cumulants of the kink number distribution present a universal scaling with the quench rate.
arXiv Detail & Related papers (2022-07-08T09:55:05Z) - Review on coherent quantum emitters in hexagonal boron nitride [91.3755431537592]
I discuss the state-of-the-art of defect centers in hexagonal boron nitride with a focus on optically coherent defect centers.
The spectral transition linewidth remains unusually narrow even at room temperature.
The field is put into a broad perspective with impact on quantum technology such as quantum optics, quantum photonics as well as spin optomechanics.
arXiv Detail & Related papers (2022-01-31T12:49:43Z) - Probing chiral edge dynamics and bulk topology of a synthetic Hall
system [52.77024349608834]
Quantum Hall systems are characterized by the quantization of the Hall conductance -- a bulk property rooted in the topological structure of the underlying quantum states.
Here, we realize a quantum Hall system using ultracold dysprosium atoms, in a two-dimensional geometry formed by one spatial dimension.
We demonstrate that the large number of magnetic sublevels leads to distinct bulk and edge behaviors.
arXiv Detail & Related papers (2020-01-06T16:59:08Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.