Unveiling Non-Hermitian Spectral Topology in Hyperbolic Lattices with Non-Abelian Translation Symmetry

• URL: http://arxiv.org/abs/2412.05607v1
• Date: Sat, 07 Dec 2024 10:33:53 GMT
• Title: Unveiling Non-Hermitian Spectral Topology in Hyperbolic Lattices with Non-Abelian Translation Symmetry
• Authors: Mengying Hu, Jing Lin, Kun Ding,
• Abstract summary: We develop an approach to determining the spectra under open boundary conditions (OBCs) from the reciprocal space of hyperbolic lattices (HBLs)<n>By introducing supercells to encompass states that are allowed by non-Abelian translational groups, we perform analytic continuation and base on the point gap topology to acquire uniform spectra.<n>Applying this method to a single-band nonreciprocal model and a reciprocal non-Abelian semimetal model, we reveal higher-dimensional skin effects and topological phase transitions.
• Score: 5.889732092453942
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The hyperbolic lattice (HBL) has emerged as a compelling platform for exploring matter in non-Euclidean space. Among its notable features, the breakdown of the conventional Bloch theorem stands out, prompting a reexamination of band theory, with the determination of spectra for non-Hermitian systems being a prominent example. Here, we develop an approach to determining the spectra under open boundary conditions (OBCs), one of the foundations in non-Hermitian lattices, from the reciprocal space of HBLs. By introducing supercells to encompass states that are allowed by non-Abelian translational groups, we perform analytic continuation and base on the point gap topology to acquire uniform spectra, the universal OBC spectral range. Applying this method to a single-band nonreciprocal model and a reciprocal non-Abelian semimetal model, we reveal higher-dimensional skin effects and topological phase transitions, respectively, demonstrating the feasibility of our method in predicting spectral topology and investigating non-Hermitian physics in HBLs.

Related papers

• Avoided-crossings, degeneracies and Berry phases in the spectrum of quantum noise through analytic Bloch-Messiah decomposition [49.1574468325115]
  "analytic Bloch-Messiah decomposition" provides approach for characterizing dynamics of quantum optical systems. We show that avoided crossings arise naturally when a single parameter is varied, leading to hypersensitivity of the singular vectors. We highlight the possibility of programming the spectral response of photonic systems through the deliberate design of avoided crossings.
  arXiv  Detail & Related papers  (2025-04-29T13:14:15Z)
• Nonlinearity-driven Topology via Spontaneous Symmetry Breaking [79.16635054977068]
  We consider a chain of parametrically-driven quantum resonators coupled only via weak nearest-neighbour cross-Kerr interaction. Topology is dictated by the structure of the Kerr nonlinearity, yielding a non-trivial bulk-boundary correspondence.
  arXiv  Detail & Related papers  (2025-03-15T00:20:45Z)
• Brickwall One-Loop Determinant: Spectral Statistics & Krylov Complexity [0.0]
  We show that the brickwall model exhibits features consistent with random matrix theory across various ensembles. We also identify signatures of integrability at extreme values of the Dirichlet boundary condition parameter.
  arXiv  Detail & Related papers  (2024-12-16T19:12:59Z)
• Quench Spectroscopy for Dissipative and (Non)-Hermitian Quantum Lattice Models [0.0]
  We extend the quench spectroscopy method to dissipative and isolated non-Hermitian quantum lattice models. We first investigate theoretically the dynamics of the open Bose-Hubbard chain confined in the superfluid phase induced by a sudden global quench. We then discuss the applicability of the quench spectroscopy to non-Hermitian transverse-field Ising chain confined in the paramagnetic phase.
  arXiv  Detail & Related papers  (2024-12-01T01:24:11Z)
• 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)
• Non-chiral non-Bloch invariants and topological phase diagram in non-unitary quantum dynamics without chiral symmetry [26.179241616332387]
  We identify the non-Bloch topological phase diagram of a one-dimensional (1D) non-Hermitian system without chiral symmetry. We find that such topological invariants can distinguish topologically distinct gapped phases. Our work provides a useful platform to study the interplay among topology, symmetries and the non-Hermiticity.
  arXiv  Detail & Related papers  (2024-07-26T03:29:30Z)
• Interacting chiral fermions on the lattice with matrix product operator norms [37.69303106863453]
  We develop a Hamiltonian formalism for simulating interacting chiral fermions on the lattice. The fermion doubling problem is circumvented by constructing a Fock space endowed with a semi-definite norm. We demonstrate that the scaling limit of the free model recovers the chiral fermion field.
  arXiv  Detail & Related papers  (2024-05-16T17:46:12Z)
• Non-Bloch dynamics and topology in a classical non-equilibrium process [6.787112704740002]
  The non-Hermitian skin effect refers to the accumulation of eigenstates near the boundary in open boundary lattice models. Our study highlights the significant and general role of non-Bloch topology in non-equilibrium dynamics.
  arXiv  Detail & Related papers  (2023-06-19T18:15:03Z)
• Measurement phase transitions in the no-click limit as quantum phase transitions of a non-hermitean vacuum [77.34726150561087]
  We study phase transitions occurring in the stationary state of the dynamics of integrable many-body non-Hermitian Hamiltonians. We observe that the entanglement phase transitions occurring in the stationary state have the same nature as that occurring in the vacuum of the non-hermitian Hamiltonian.
  arXiv  Detail & Related papers  (2023-01-18T09:26:02Z)
• Non-Hermitian spectral flows and Berry-Chern monopoles [0.0]
  We show a non-Hermitian generalization of the correspondence between the spectral flow and the topological charges of band crossing points. A class of non-Hermitian Hamiltonians that display a complex-valued spectral flow is built by deforming an Hermitian model.
  arXiv  Detail & Related papers  (2022-09-08T15:27:49Z)
• Simulation of absorption spectra of molecular aggregates: a Hierarchy of Stochastic Pure States approach [68.8204255655161]
  hierarchy of pure states (HOPS) provides a formally exact solution based on local, trajectories. Exploiting the localization of HOPS for the simulation of absorption spectra in large aggregares requires a formulation in terms of normalized trajectories.
  arXiv  Detail & Related papers  (2021-11-01T16:59:54Z)
• The topological counterparts of non-Hermitian SSH models [0.0]
  We propose a method to construct the topological equivalent models of the non-Hermitian dimerized lattices with the similarity transformations. As an illustration, we apply this approach to several representative non-Hermitian SSH models.
  arXiv  Detail & Related papers  (2021-03-23T08:58:43Z)
• Spectral properties of relativistic quantum waveguides [0.0]
  We find an effective Hamiltonian on the base curve which approximates the original operator in the thin-strip limit. We also investigate the existence of bound states in the non-relativistic limit and give a geometric condition for the bound states to exist.
  arXiv  Detail & Related papers  (2021-01-11T16:33:52Z)
• Quantum particle across Grushin singularity [77.34726150561087]
  We study the phenomenon of transmission across the singularity that separates the two half-cylinders. All the local realisations of the free (Laplace-Beltrami) quantum Hamiltonian are examined as non-equivalent protocols of transmission/reflection. This allows to comprehend the distinguished status of the so-called bridging' transmission protocol previously identified in the literature.
  arXiv  Detail & Related papers  (2020-11-27T12:53:23Z)
• Operator-algebraic renormalization and wavelets [62.997667081978825]
  We construct the continuum free field as the scaling limit of Hamiltonian lattice systems using wavelet theory. A renormalization group step is determined by the scaling equation identifying lattice observables with the continuum field smeared by compactly supported wavelets.
  arXiv  Detail & Related papers  (2020-02-04T18:04:51Z)
• Bulk detection of time-dependent topological transitions in quenched chiral models [48.7576911714538]
  We show that the winding number of the Hamiltonian eigenstates can be read-out by measuring the mean chiral displacement of a single-particle wavefunction. This implies that the mean chiral displacement can detect the winding number even when the underlying Hamiltonian is quenched between different topological phases.
  arXiv  Detail & Related papers  (2020-01-16T17:44:52Z)

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.