Detecting bulk and edge exceptional points in non-Hermitian systems through generalized Petermann factors

• URL: http://arxiv.org/abs/2208.14944v3
• Date: Thu, 20 Apr 2023 14:49:46 GMT
• Title: Detecting bulk and edge exceptional points in non-Hermitian systems through generalized Petermann factors
• Authors: Yue-Yu Zou, Yao Zhou, Li-Mei Chen, Peng Ye
• Abstract summary: Non-orthogonality in non-Hermitian quantum systems gives rise to tremendous exotic quantum phenomena. We introduce an interesting quantity (denoted as $eta$) as a new variant of the Petermann factor to measure non-unitarity.
• Score: 7.371841894852217
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Non-orthogonality in non-Hermitian quantum systems gives rise to tremendous exotic quantum phenomena, which can be fundamentally traced back to non-unitarity and is much more fundamental and universal than complex energy spectrum. In this paper, we introduce an interesting quantity (denoted as $\eta$) as a new variant of the Petermann factor to directly and efficiently measure non-unitarity and the associated non-Hermitian physics. By tuning the model parameters of underlying non-Hermitian systems, we find that the discontinuity of both $\eta$ and its first-order derivative (denoted as $\partial \eta$) pronouncedly captures rich physics that is fundamentally caused by non-unitarity. More concretely, in the 1D non-Hermitian topological systems, two mutually orthogonal edge states that are respectively localized on two boundaries become non-orthogonal in the vicinity of discontinuity of $\eta$ as a function of the model parameter, which is dubbed ``edge state transition''. Through theoretical analysis, we identify that the appearance of edge state transition indicates the existence of exceptional points~(EPs) in topological edge states. Regarding the discontinuity of $\partial\eta$, we investigate a two-level non-Hermitian model and establish a connection between the points of discontinuity of $\partial \eta$ and EPs of bulk states. By studying this connection in more general lattice models, we find that some models have discontinuity of $\partial\eta$, implying the existence of EPs in bulk states.

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)
• Tunable quantum criticality and pseudocriticality across the fixed-point annihilation in the anisotropic spin-boson model [0.26107298043931204]
  We study the nontrivial renormalization-group scenario of fixed-point annihilation in spin-boson models. We find a tunable transition between two localized phases that can be continuous or strongly first-order. We also find scaling behavior at the symmetry-enhanced first-order transition, for which the inverse correlation-length exponent is given by the bath exponent.
  arXiv  Detail & Related papers  (2024-03-04T19:00:07Z)
• Non-Hermitian extended midgap states and bound states in the continuum [0.0]
  We find two flavours of bound states in the continuum, both stable even in the absence of chiral symmetry. Results clarify fundamental aspects of topology, and symmetry in the light of different approaches to the anomalous non-Hermitan bulk-boundary correspondence.
  arXiv  Detail & Related papers  (2023-10-27T16:58:04Z)
• Exceptional entanglement in non-Hermitian fermionic models [1.8853792538756093]
  Exotic singular objects, known as exceptional points, are ubiquitous in non-Hermitian physics. From the entanglement spectrum, zero-energy exceptional modes are found to be distinct from normal zero modes or topological boundary modes.
  arXiv  Detail & Related papers  (2023-04-13T12:40:11Z)
• 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-zero momentum requires long-range entanglement [6.018940870331878]
  We show that a quantum state in a lattice spin (boson) system must be long-range entangled if it has non-zero lattice momentum. The statement can also be generalized to fermion systems.
  arXiv  Detail & Related papers  (2021-12-13T19:00:04Z)
• 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)
• Non-equilibrium stationary states of quantum non-Hermitian lattice models [68.8204255655161]
  We show how generic non-Hermitian tight-binding lattice models can be realized in an unconditional, quantum-mechanically consistent manner. We focus on the quantum steady states of such models for both fermionic and bosonic systems.
  arXiv  Detail & Related papers  (2021-03-02T18:56:44Z)
• Non-Hermitian N-state degeneracies: unitary realizations via antisymmetric anharmonicities [0.0]
  degeneracy of an $N-$plet of bound states is studied in the framework of quantum theory of closed (i.e., unitary) systems. For an underlying Hamiltonian $H=H(lambda)$ the degeneracy occurs at a Kato's exceptional point.
  arXiv  Detail & Related papers  (2020-10-28T14:41:52Z)
• 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)
• Anisotropy-mediated reentrant localization [62.997667081978825]
  We consider a 2d dipolar system, $d=2$, with the generalized dipole-dipole interaction $sim r-a$, and the power $a$ controlled experimentally in trapped-ion or Rydberg-atom systems. We show that the spatially homogeneous tilt $beta$ of the dipoles giving rise to the anisotropic dipole exchange leads to the non-trivial reentrant localization beyond the locator expansion.
  arXiv  Detail & Related papers  (2020-01-31T19:00:01Z)

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.