Absolutely Continuous Edge Spectrum of Hall Insulators on the Lattice

• URL: http://arxiv.org/abs/2101.08603v1
• Date: Thu, 21 Jan 2021 13:42:01 GMT
• Title: Absolutely Continuous Edge Spectrum of Hall Insulators on the Lattice
• Abstract summary: The presence of chiral modes on the edges of quantum Hall samples is essential to our understanding of the quantum Hall effect. We show that if a free fermion system on the two-dimensional lattice is gapped in the bulk, and has a nonvanishing Hall conductance, then the same system put on a half-space geometry supports edge modes whose spectrum fills the entire bulk gap and is absolutely continuous.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The presence of chiral modes on the edges of quantum Hall samples is essential to our understanding of the quantum Hall effect. In particular, these edge modes should support ballistic transport and therefore, in a single particle picture, be supported in the absolutely continuous spectrum of the single-particle Hamiltonian. We show in this note that if a free fermion system on the two-dimensional lattice is gapped in the bulk, and has a nonvanishing Hall conductance, then the same system put on a half-space geometry supports edge modes whose spectrum fills the entire bulk gap and is absolutely continuous.

Related papers

• Exact analytical spectrum, eigenstates, and quantum geometry of the quarter-flux Harper-Hofstadter model [0.0]
  Quantum geometry has emerged as a guiding principle across atomic and condensed-matter physics.<n>We provide closed-form expressions for both the spectrum and the quantum geometry of a paradigmatic four-band model.<n>We evaluate fractional-Chern-insulator stability criteria analytically and quantify the lowest band of the quarter-flux Harper-Hofstadter model to be a nearly ideal Chern band.
  arXiv  Detail & Related papers  (2026-08-26T17:58:52Z)
• Bound, antibound and resonance two-photon states in chiral waveguide QED [51.56484100374058]
  We present a theoretical study of the two-particle spectrum $(K)$ for the chiral waveguide QED setup.<n>For each pair center-of-mass momentum $K$ there exist distinct solutions with $Imle 0$ in the two-particle spectrum.<n>An interesting finding is that the real part of the spectrum $Re (K)$ in the chiral model is gapless.
  arXiv  Detail & Related papers  (2026-04-22T14:19:46Z)
• Unified Integer and Fractional Quantum Hall Effects from Boundary-Induced Edge-State Quantization [0.0]
  We show that boundary-induced quantization of edge states provides a missing bridge between bulk quantization and the hierarchy of quantum Hall plateaus.<n>Results establish boundary-induced quantization as the microscopic origin of quantum Hall transport.
  arXiv  Detail & Related papers  (2026-03-04T22:28:13Z)
• Emergent cavity-QED dynamics along the edge of a photonic lattice [0.29022435221103454]
  We show that light matter interactions are effectively captured by a dissipative cavity QED model.<n>We predict occurrence of vacuum Rabi oscillations and efficient state transfer between distant emitters.
  arXiv  Detail & Related papers  (2025-07-17T18:00:03Z)
• Quantum Hall Effect without Chern Bands [0.0]
  The quantum Hall effect was originally observed in a two-dimensional electron gas forming Landau levels when exposed to a strong magnetic field.<n>We report on the robust occurrence of an integer quantized transverse conductance at the onset of disorder in a microscopic lattice model.
  arXiv  Detail & Related papers  (2025-05-14T18:00:01Z)
• Absolutely continuous spectrum for truncated topological insulators [0.0]
  We show that if a topological insulator is truncated along a curve that separates the plane in two sufficiently large regions, the edge system admits absolutely continuous spectrum. Our approach combines a recent version of the bulk-edge correspondence along curves that separates geometry and intrinsic conductance.
  arXiv  Detail & Related papers  (2024-10-03T02:39:57Z)
• Flat-band induced local Hilbert space fragmentation [0.0]
  We show that a class of flat-band lattices with underlying commutative local symmetries exhibit a locally fragmented Hilbert space. We analyze the fragmentation of the one-dimensional Pyrochlore chain, which exhibits both nonintegrable sectors, effective single-particle sectors, and frozen states.
  arXiv  Detail & Related papers  (2023-06-27T17:55:04Z)
• 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)
• Fermion production at the boundary of an expanding universe: a cold-atom gravitational analogue [68.8204255655161]
  We study the phenomenon of cosmological particle production of Dirac fermions in a Friedman-Robertson-Walker spacetime. We present a scheme for the quantum simulation of this gravitational analogue by means of ultra-cold atoms in Raman optical lattices.
  arXiv  Detail & Related papers  (2022-12-02T18:28:23Z)
• Quantum vibrational mode in a cavity confining a massless spinor field [91.3755431537592]
  We analyse the reaction of a massless (1+1)-dimensional spinor field to the harmonic motion of one cavity wall. We demonstrate that the system is able to convert bosons into fermion pairs at the lowest perturbative order.
  arXiv  Detail & Related papers  (2022-09-12T08:21:12Z)
• The frustration-free fully packed loop model [4.965221313169878]
  We consider a quantum fully packed loop model on the square lattice with a frustration-free projector Hamiltonian and ring-exchange interactions acting on plaquettes. We discuss how the boundary term fractures the Hilbert space into Krylov subspaces, and we prove that the Hamiltonian is ergodic within each subspace. We show that the spectrum is shown to be gapless in the thermodynamic limit with a trial state constructed by adding a twist to the ground state superposition.
  arXiv  Detail & Related papers  (2022-06-03T18:00:04Z)
• Bosonic fractional quantum Hall conductance in shaken honeycomb optical lattices without flat bands [0.45263443016057897]
  We propose a scheme to realize bosonic fractional quantum Hall conductance in shaken honeycomb optical lattices. By filling the lattice at 1/4 with identical bosons under Feshbach resonance, two degenerate many-body ground states share one Chern number of 1. We prove that the fractional quantum Hall state can be prepared by adiabatically turning on the lattice shaking, and the fractional conductance is robust in the shaken lattice.
  arXiv  Detail & Related papers  (2021-10-22T04:49:00Z)
• Fano Resonances in Quantum Transport with Vibrations [50.591267188664666]
  Quantum mechanical scattering continuum states coupled to a scatterer with a discrete spectrum gives rise to Fano resonances. We consider scatterers that possess internal vibrational degrees of freedom in addition to discrete states.
  arXiv  Detail & Related papers  (2021-08-07T12:13:59Z)
• Tight-Binding realization of non-abelian gauge fields: singular spectra and wave confinement [0.0]
  We present a geometric construction of a lattice that emulates the action of a gauge field on a fermion. The emulation covers both abelian and non-abelian gauge fields.
  arXiv  Detail & Related papers  (2021-06-09T22:15:24Z)
• Fano interference in quantum resonances from angle-resolved elastic scattering [62.997667081978825]
  We show that probing the angular dependence of the cross section allows us to unveil asymmetric Fano profiles in a single channel shape resonance. We observe a shift in the peak of the resonance profile in the elastic collisions between metastable helium and deuterium molecules.
  arXiv  Detail & Related papers  (2021-05-12T20:41:25Z)
• 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)

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.