Braid Protected Topological Band Structures with Unpaired Exceptional Points

• URL: http://arxiv.org/abs/2211.05788v2
• Date: Sun, 29 Oct 2023 13:49:32 GMT
• Title: Braid Protected Topological Band Structures with Unpaired Exceptional Points
• Authors: J. Lukas K. K\"onig, Kang Yang, Jan Carl Budich and Emil J. Bergholtz
• Abstract summary: We show the existence of topologically stable unpaired exceptional points (EPs) We derive how noncommuting braids of complex energy levels may stabilize unpaired EPs.
• Score: 3.403098273287476
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We demonstrate the existence of topologically stable unpaired exceptional points (EPs), and construct simple non-Hermitian (NH) tight-binding models exemplifying such remarkable nodal phases. While fermion doubling, i.e. the necessity of compensating the topological charge of a stable nodal point by an anti-dote, rules out a direct counterpart of our findings in the realm of Hermitian semimetals, here we derive how noncommuting braids of complex energy levels may stabilize unpaired EPs. Drawing on this insight, we reveal the occurrence of a single, unpaired EP, manifested as a non-Abelian monopole in the Brillouin zone of a minimal three-band model. This third-order degeneracy represents a sweet spot within a larger topological phase that cannot be fully gapped by any local perturbation. Instead, it may only split into simpler (second-order) degeneracies that can only gap out by pairwise annihilation after having moved around inequivalent large circles of the Brillouin zone. Our results imply the incompleteness of a topological classification based on winding numbers, due to non-Abelian representations of the braid group intertwining three or more complex energy levels, and provide insights into the topological robustness of non-Hermitian systems and their non-Abelian phase transitions.

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)
• Braids and Higher-order Exceptional Points from the Interplay Between Lossy Defects and Topological Boundary States [1.9747483000555663]
  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.
  arXiv  Detail & Related papers  (2023-12-05T19:00:00Z)
• Non-Gaussian superradiant transition via three-body ultrastrong coupling [62.997667081978825]
  We introduce a class of quantum optical Hamiltonian characterized by three-body couplings. We propose a circuit-QED scheme based on state-of-the-art technology that implements the considered model.
  arXiv  Detail & Related papers  (2022-04-07T15:39:21Z)
• Topological Anderson insulators with different bulk states in quasiperiodic chains [1.6530012863603747]
  We investigate the topology and localization of one-dimensional Hermitian and non-Hermitian Su-Schrieffer-Heeger chains with quasiperiodic hopping modulations. We show the presence of topological extended, intermediate, and localized phases due to the coexistence of independent topological and localization phase transitions.
  arXiv  Detail & Related papers  (2022-01-04T05:32:43Z)
• Topological transitions with continuously monitored free fermions [68.8204255655161]
  We show the presence of a topological phase transition that is of a different universality class than that observed in stroboscopic projective circuits. We find that this entanglement transition is well identified by a combination of the bipartite entanglement entropy and the topological entanglement entropy.
  arXiv  Detail & Related papers  (2021-12-17T22:01:54Z)
• Non-Hermitian $C_{NH} = 2$ Chern insulator protected by generalized rotational symmetry [85.36456486475119]
  A non-Hermitian system is protected by the generalized rotational symmetry $H+=UHU+$ of the system. Our finding paves the way towards novel non-Hermitian topological systems characterized by large values of topological invariants.
  arXiv  Detail & Related papers  (2021-11-24T15:50:22Z)
• Illuminating the bulk-boundary correspondence of a non-Hermitian stub lattice with Majorana stars [0.0]
  We analyze the topological phases of a nonreciprocal hopping model on the stub lattice. The parity of the total azimuthal winding of the entire Majorana constellation correctly predicts the appearance of edge states between the bulk gaps.
  arXiv  Detail & Related papers  (2021-08-27T16:09:27Z)
• Topology of anti-parity-time-symmetric non-Hermitian Su-Schrieffer-Heeger model [0.0]
  We show that the large non-Hermiticity constructively creates nontrivial topology and greatly expands the topological phase. Our findings can be verified through introducing dissipations in every another two sites of the standard SSH model even in its trivial phase.
  arXiv  Detail & Related papers  (2021-05-08T11:17:08Z)
• Large Chern numbers in a dissipative dice model [0.0]
  We show that the topological phases are protected by the real gaps and the bulk-edge correspondence. We find that there are topological non-trivial phases with large Chern numbers $C=-3$ robust against the dissipative perturbations.
  arXiv  Detail & Related papers  (2020-09-12T10:54:42Z)
• Quantum anomalous Hall phase in synthetic bilayers via twistless twistronics [58.720142291102135]
  We propose quantum simulators of "twistronic-like" physics based on ultracold atoms and syntheticdimensions. We show that our system exhibits topologicalband structures under appropriate conditions.
  arXiv  Detail & Related papers  (2020-08-06T19:58:05Z)
• 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.