Non-Hermitian Origin of Wannier Localizability and Detachable Topological Boundary States

• URL: http://arxiv.org/abs/2407.09458v2
• Date: Mon, 22 Jul 2024 14:25:40 GMT
• Title: Non-Hermitian Origin of Wannier Localizability and Detachable Topological Boundary States
• Authors: Daichi Nakamura, Ken Shiozaki, Kenji Shimomura, Masatoshi Sato, Kohei Kawabata,
• Abstract summary: We identify non-Hermitian boundary states as detachable topological boundary states. We show that intrinsic non-Hermitian topology leads to the inevitable spectral flow. Based on this connection and $K$-theory, we complete the classification of Wannier localizability and detachable topological boundary states.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: While topology can impose obstructions to exponentially localized Wannier functions, certain topological insulators are exempt from such Wannier obstructions. The absence of the Wannier obstructions can further accompany topological boundary states that are detachable from the bulk bands. Here, we elucidate a close connection between these detachable topological boundary states and non-Hermitian topology. Identifying topological boundary states as non-Hermitian topology, we demonstrate that intrinsic non-Hermitian topology leads to the inevitable spectral flow. By contrast, we show that extrinsic non-Hermitian topology underlies the detachment of topological boundary states and clarify anti-Hermitian topology of the detached boundary states. Based on this connection and $K$-theory, we complete the tenfold classification of Wannier localizability and detachable topological boundary states.

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)
• $K$-theory classification of Wannier localizability and detachable topological boundary states [0.0]
  We show that non-Hermitian topology underlies detachable boundary states in Hermitian topological insulators and superconductors. We classify Wannier localizability through the homomorphisms of topological phases from the tenfold Altland-Zirnbauer symmetry classes to the threefold Wigner-Dyson symmetry classes.
  arXiv  Detail & Related papers  (2024-07-23T07:27:41Z)
• 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)
• Injection and nucleation of topological defects in the quench dynamics of the Frenkel-Kontorova model [30.733286944793527]
  Topological defects have strong impact on both elastic and inelastic properties of materials. We investigate the possibility to controllably inject topological defects in quantum simulators of solid state lattice structures.
  arXiv  Detail & Related papers  (2022-10-26T17:59:57Z)
• 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)
• Bulk-boundary correspondence in point-gap topological phases [0.0]
  A striking feature of non-Hermitian systems is the presence of two different types of topology. One generalizes Hermitian topological phases, the other is intrinsic to non-Hermitian systems. This Letter establishes the bulk-boundary correspondence in the point-gap topology in non-Hermitian systems.
  arXiv  Detail & Related papers  (2022-05-31T09:26:44Z)
• Selective and tunable excitation of topological non-Hermitian skin modes [0.0]
  Non-Hermitian lattices sustain an extensive number of exponentially-localized states, dubbed non-Hermitian skin modes. Such states can be predicted from the nontrivial topology of the energy spectrum under periodic boundary conditions. In any realistic system with a finite lattice size most of skin edge states collapse and become metastable states.
  arXiv  Detail & Related papers  (2021-12-09T15:32:39Z)
• Extrinsic topology of Floquet anomalous boundary states in quantum walks [0.0]
  We find that Floquet anomalous boundary states in quantum walks have similar extrinsic topological natures. In contrast to higher order topological insulators, the extrinsic topology in quantum walks is manifest even for first-order topological phases.
  arXiv  Detail & Related papers  (2021-12-06T16:56:28Z)
• 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)
• 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.