Braids and Higher-order Exceptional Points from the Interplay Between Lossy Defects and Topological Boundary States

• URL: http://arxiv.org/abs/2312.03054v2
• Date: Sun, 13 Oct 2024 15:36:26 GMT
• Title: Braids and Higher-order Exceptional Points from the Interplay Between Lossy Defects and Topological Boundary States
• Authors: Zi-Jian Li, Gabriel Cardoso, Emil J. Bergholtz, Qing-Dong Jiang,
• Abstract summary: We show that the perturbation of the Su-Schrieffer-Heeger chain by a localized lossy defect leads to higher-order exceptional points (HOEP) On the one hand, they arise due to the non-Abelian braiding properties of exceptional lines (EL) in parameter space. On the other hand, we show that such special intersections happen due to the fact that the delocalization of edge states, induced by the non-Hermitian defect, hybridizes them with defect states.
• Score: 1.9747483000555663
• License:
• Abstract: We show that the perturbation of the Su-Schrieffer-Heeger chain by a localized lossy defect leads to higher-order exceptional points (HOEP). Depending on the location of the defect, third- and fourth- order exceptional points (EP3 \& EP4) appear in the space of Hamiltonian parameters. On the one hand, they arise due to the non-Abelian braiding properties of exceptional lines (EL) in parameter space. Namely, the HOEPs lie at intersections of mutually non-commuting ELs. On the other hand, we show that such special intersections happen due to the fact that the delocalization of edge states, induced by the non-Hermitian defect, hybridizes them with defect states. These can then coalesce together into an EP3. When the defect lies at the midpoint of the chain, a special symmetry of the full spectrum can lead to an EP4. In this way, our model illustrates the emergence of interesting non-Abelian topological properties in the multiband structure of non-Hermitian perturbations of topological phases.

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)
• Critical spin models from holographic disorder [49.1574468325115]
  We study the behavior of XXZ spin chains with a quasiperiodic disorder not present in continuum holography. Our results suggest the existence of a class of critical phases whose symmetries are derived from models of discrete holography.
  arXiv  Detail & Related papers  (2024-09-25T18:00:02Z)
• Braid Protected Topological Band Structures with Unpaired Exceptional Points [3.403098273287476]
  We show the existence of topologically stable unpaired exceptional points (EPs) We derive how noncommuting braids of complex energy levels may stabilize unpaired EPs.
  arXiv  Detail & Related papers  (2022-11-10T19:00:00Z)
• Symmetry-protected exceptional and nodal points in non-Hermitian systems [0.0]
  We show that NH systems may host two types of degeneracies, namely, non-defective EPs and ordinary (Hermitian) nodal points. We demonstrate that certain discrete symmetries, namely parity-time, parity-particle-hole, and pseudo-Hermitian symmetry, guarantee the occurrence of both defective and non-defective EPs.
  arXiv  Detail & Related papers  (2022-04-29T08:42:26Z)
• Symmetry protected exceptional points of interacting fermions [0.0]
  Non-hermitian quantum systems can exhibit spectral degeneracies known as exceptional points, where two or more eigenvectors coalesce. We investigate the fate of such symmetry protected exceptional points in the presence of a symmetry preserving interaction between fermions. We also find that exceptional points can annihilate each other if they meet in parameter space with compatible many-body states forming a third order exceptional point at the endpoint.
  arXiv  Detail & Related papers  (2022-04-11T18:00:52Z)
• Locality of Spontaneous Symmetry Breaking and Universal Spacing Distribution of Topological Defects Formed Across a Phase Transition [62.997667081978825]
  A continuous phase transition results in the formation of topological defects with a density predicted by the Kibble-Zurek mechanism (KZM) We characterize the spatial distribution of point-like topological defects in the resulting nonequilibrium state and model it using a Poisson point process in arbitrary spatial dimension with KZM density.
  arXiv  Detail & Related papers  (2022-02-23T19:00:06Z)
• Spectrum of localized states in fermionic chains with defect and adiabatic charge pumping [68.8204255655161]
  We study the localized states of a generic quadratic fermionic chain with finite-range couplings. We analyze the robustness of the connection between bands against perturbations of the Hamiltonian.
  arXiv  Detail & Related papers  (2021-07-20T18:44:06Z)
• Symmetry-protected multifold exceptional points and their topological characterization [0.0]
  We investigate the existence of higher order exceptional points (EPs) in non-Hermitian systems. We show that $mu$-fold EPs are stable in $mu-1$ dimensions in the presence of anti-unitary symmetries. We show different non-Hermitian topological transitions associated with these exceptional points, such as their merging and a transition to a regime where propagation becomes forbidden.
  arXiv  Detail & Related papers  (2021-03-15T09:31:14Z)
• Observation of Hermitian and Non-Hermitian Diabolic Points and Exceptional Rings in Parity-Time symmetric ZRC and RLC Dimers [62.997667081978825]
  We show how appears non-Hermitian degeneracy points in the spectrum and how they are protected against a Hermitian perturbation. This work opens a gold road for investigations on topological electrical circuits for robust transport of information at room temperature.
  arXiv  Detail & Related papers  (2020-04-17T15:51:49Z)
• 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.