Illuminating the bulk-boundary correspondence of a non-Hermitian stub lattice with Majorana stars

• URL: http://arxiv.org/abs/2108.12372v2
• Date: Mon, 15 Nov 2021 19:25:26 GMT
• Title: Illuminating the bulk-boundary correspondence of a non-Hermitian stub lattice with Majorana stars
• Authors: James Bartlett, Haiping Hu, Erhai Zhao
• Abstract summary: 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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Topological characterization of non-Hermitian band structures demands more than a straightforward generalization of the Hermitian cases. Even for one-dimensional tight-binding models with nonreciprocal hopping, the appearance of point gaps and the skin effect leads to the breakdown of the usual bulk-boundary correspondence. Luckily, the correspondence can be resurrected by introducing a winding number for the generalized Brillouin zone for systems with even number of bands and chiral symmetry. Here, we analyze the topological phases of a nonreciprocal hopping model on the stub lattice, where one of the three bands remains flat. Due to the lack of chiral symmetry, the biorthogonal Zak phase is no longer quantized, invalidating the winding number as a topological index. Instead, we show that a $Z_2$ invariant can be defined from Majorana's stellar representation of the eigenstates on the Bloch sphere. The parity of the total azimuthal winding of the entire Majorana constellation correctly predicts the appearance of edge states between the bulk gaps. We further show that the system is not a square-root topological insulator, despite the fact that its parent Hamiltonian can be block diagonalized and related to a sawtooth lattice model. The analysis presented here may be generalized to understand other non-Hermitian systems with multiple bands.

Related papers

• A holographic view of topological stabilizer codes [0.6290982779160698]
  We provide an explicit and general framework for understanding the bulk-boundary correspondence in Pauli topological stabilizer codes. We show that the boundary Hilbert space cannot be realized via local degrees of freedom. We show how linear and fractal subsystem symmetries naturally arise at the boundaries of fracton phases.
  arXiv  Detail & Related papers  (2023-12-07T19:00:00Z)
• Softening of Majorana edge states by long-range couplings [77.34726150561087]
  Long-range couplings in the Kitaev chain is shown to modify the universal scaling of topological states close to the critical point. We prove that the Majorana states become increasingly delocalised at a universal rate which is only determined by the interaction range.
  arXiv  Detail & Related papers  (2023-01-29T19:00:08Z)
• Hermitian Topologies originating from non-Hermitian braidings [0.0]
  We show that the complex energy bands of non-Hermitian systems braid in momentum space even in one dimension. We derive an elegant identity that equates the linking number between the knots of braiding non-Hermitian bands and the zero-energy loop. We construct typical topological phases with non-Hermitian braidings, which can be readily realized by artificial crystals.
  arXiv  Detail & Related papers  (2022-12-28T08:08:58Z)
• Unravelling the edge spectra of non-Hermitian Chern insulators [0.0]
  Non-Hermitian Chern insulators differ from their Hermitian cousins in one key aspect: their edge spectra are incredibly rich and confounding. We outline how such a theory can be set up to yield a thorough understanding of the edge phase diagram. The approach presented here can be generalized to more complicated models of non-Hermitian insulators or semimetals in two or three dimensions.
  arXiv  Detail & Related papers  (2022-09-14T16:52:16Z)
• 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)
• 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)
• Boundary theories of critical matchgate tensor networks [59.433172590351234]
  Key aspects of the AdS/CFT correspondence can be captured in terms of tensor network models on hyperbolic lattices. For tensors fulfilling the matchgate constraint, these have previously been shown to produce disordered boundary states. We show that these Hamiltonians exhibit multi-scale quasiperiodic symmetries captured by an analytical toy model.
  arXiv  Detail & Related papers  (2021-10-06T18:00:03Z)
• 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)
• Frustration-free Hamiltonian with Topological Order on Graphs [1.933681537640272]
  It is commonly believed that models defined on a closed one-dimensional manifold cannot give rise to topological order. Here we construct frustration-free Hamiltonians which possess both symmetry protected topological order (SPT) and multiple ground state degeneracy (GSD) Instead of global symmetry breaking, there exists a it local symmetry operator that commutes with the Hamiltonian and connects the multiple ground states.
  arXiv  Detail & Related papers  (2020-12-09T09:19:27Z)
• 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)
• Topological characterization of non-Hermitian multiband systems using Majorana's Stellar Representation [1.5484595752241122]
  Majorana's stellar representation (MSR) is applied to 1D multiband models consisting of asymmetric nearest-neighbor hopping and imaginary on-site potentials. The number of edge states isolated from the continuous bulk bands in the complex energy plane is successfully linked with a topological invariant constructed from MSR. Cases with the so-called non-Hermitian skin effect are also studied, showing that the bulk-boundary correspondence between our defined winding numbers and isolated edge states can be restored.
  arXiv  Detail & Related papers  (2020-02-18T11:15:47Z)

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.