Non-Hermitian topological phenomena: A review

• URL: http://arxiv.org/abs/2205.10379v1
• Date: Fri, 20 May 2022 18:00:02 GMT
• Title: Non-Hermitian topological phenomena: A review
• Authors: Nobuyuki Okuma and Masatoshi Sato
• Abstract summary: We review developments in non-Hermitian topological physics by focusing mainly on the boundary problem. As well as the competition between non-Hermitian and topological boundary phenomena, we discuss the topological nature inherent in non-Hermiticity itself.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The past decades have witnessed an explosion of interest in topological materials, and a lot of mathematical concepts have been introduced in condensed matter physics. Among them, the bulk-boundary correspondence is the central topic in topological physics, which has inspired researchers to focus on boundary physics. Recently, the concepts of topological phases have been extended to non-Hermitian Hamiltonians, whose eigenvalues can be complex. Besides the topology, non-Hermiticity can also cause a boundary phenomenon called the non-Hermitian skin effect, which is an extreme sensitivity of the spectrum to the boundary condition. In this article, we review developments in non-Hermitian topological physics by focusing mainly on the boundary problem. As well as the competition between non-Hermitian and topological boundary phenomena, we discuss the topological nature inherent in non-Hermiticity itself.

Related papers

• 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)
• Non-chiral non-Bloch invariants and topological phase diagram in non-unitary quantum dynamics without chiral symmetry [26.179241616332387]
  We identify the non-Bloch topological phase diagram of a one-dimensional (1D) non-Hermitian system without chiral symmetry. We find that such topological invariants can distinguish topologically distinct gapped phases. Our work provides a useful platform to study the interplay among topology, symmetries and the non-Hermiticity.
  arXiv  Detail & Related papers  (2024-07-26T03:29:30Z)
• Gifts from long-range interaction: Emergent gapless topological behaviors in quantum spin chain [4.5353840616537555]
  Topology in condensed matter physics is typically associated with a bulk energy gap. Recent research has shifted focus to topological phases without a bulk energy gap, exhibiting nontrivial gapless topological behaviors.
  arXiv  Detail & Related papers  (2024-06-04T05:18:44Z)
• Non-Hermitian Topology in Hermitian Topological Matter [0.0]
  We show that anomalous boundary states in Hermitian topological insulators exhibit non-Hermitian topology. We also find the emergence of hinge states within effective non-Hermitian Hamiltonians at surfaces of three-dimensional topological insulators. Our work uncovers a hidden connection between Hermitian and non-Hermitian topology, and provides an approach to identifying non-Hermitian topology in quantum matter.
  arXiv  Detail & Related papers  (2024-05-16T11:59:15Z)
• Relaxation of first-class constraints and the quantization of gauge theories: from "matter without matter" to the reappearance of time in quantum gravity [72.27323884094953]
  We make a conceptual overview of an approach to the initial-value problem in canonical gauge theories. We stress how the first-class phase-space constraints may be relaxed if we interpret them as fixing the values of new degrees of freedom.
  arXiv  Detail & Related papers  (2024-02-19T19:00:02Z)
• Non-Hermitian Topological Phases: Principles and Prospects [4.3012765978447565]
  We present the key principles underpinning the features of non-Hermitian phases. We discuss exceptional points, complex energy gaps and non-Hermitian symmetry classification. We also examine the role of disorder, present the linear response framework, and analyze the Hall transport properties of non-Hermitian systems.
  arXiv  Detail & Related papers  (2022-12-13T10:57:49Z)
• Many-body topology of non-Hermitian systems [0.0]
  We show that the intrinsic non-Hermitian topological phases in one dimension survive even in the presence of many-body interactions. As an illustrative example, we investigate the interacting Hatano-Nelson model and find a unique topological phase and skin effect induced by many-body interactions.
  arXiv  Detail & Related papers  (2022-02-05T13:14:03Z)
• Bridging the gap between topological non-Hermitian physics and open quantum systems [62.997667081978825]
  We show how to detect a transition between different topological phases by measuring the response to local perturbations. Our formalism is exemplified in a 1D Hatano-Nelson model, highlighting the difference between the bosonic and fermionic cases.
  arXiv  Detail & Related papers  (2021-09-22T18:00:17Z)
• Topological Field Theory of Non-Hermitian Systems [0.0]
  We develop a field-theoretical description of the intrinsic non-Hermitian topological phases. Because of the dissipative and nonequilibrium nature of non-Hermiticity, our theory is formulated solely in terms of spatial degrees of freedom.
  arXiv  Detail & Related papers  (2020-11-23T14:50:51Z)
• Preferred basis, decoherence and a quantum state of the Universe [77.34726150561087]
  We review a number of issues in foundations of quantum theory and quantum cosmology. These issues can be considered as a part of the scientific legacy of H.D. Zeh.
  arXiv  Detail & Related papers  (2020-06-28T18:07:59Z)
• Dynamical solitons and boson fractionalization in cold-atom topological insulators [110.83289076967895]
  We study the $mathbbZ$ Bose-Hubbard model at incommensurate densities. We show how defects in the $mathbbZ$ field can appear in the ground state, connecting different sectors. Using a pumping argument, we show that it survives also for finite interactions.
  arXiv  Detail & Related papers  (2020-03-24T17:31:34Z)

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.