Unified Integer and Fractional Quantum Hall Effects from Boundary-Induced Edge-State Quantization

• URL: http://arxiv.org/abs/2603.04652v1
• Date: Wed, 04 Mar 2026 22:28:13 GMT
• Title: Unified Integer and Fractional Quantum Hall Effects from Boundary-Induced Edge-State Quantization
• Authors: Pedro Pereyra,
• Abstract summary: 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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Despite the success of Landau-level theory and edge-state transport formalisms, a direct microscopic link between bulk quantization and the observed hierarchy of quantum Hall plateaus has not been established. In particular, no unified microscopic mechanism accounting simultaneously for integer and fractional sequences has been derived within standard quantum mechanics. Here we show that boundary-induced quantization of edge states provides this missing bridge. Starting from the Landau problem in laterally confined two-dimensional electron systems, we demonstrate that the imposition of Dirichlet, Neumann, and mixed (Robin) boundary conditions discretizes both the guiding-center coordinate and the longitudinal momentum of chiral edge states. The resulting boundary-dependent spectra generate families of edge channels with well-defined multiplicities that couple to electronic transport. When incorporated into an edge-state transport description, this boundary quantization reproduces the integer Hall sequence and simultaneously yields a structured hierarchy of fractional filling factors without invoking separate microscopic mechanisms. We further show that a weak Hall-induced parity-breaking contribution reorganizes the low-energy edge spectrum while leaving the bulk Landau levels intact. This controlled symmetry breaking enhances edge-state multiplicities at small Landau indices and stabilizes the fractional plateaus observed at strong magnetic fields. The quantized Hall response thus emerges from the interplay between Landau quantization and boundary-induced guiding-center discretization, which together determine the spectrum and occupation of chiral edge channels. These results establish boundary-induced quantization as the microscopic origin of quantum Hall transport and provide a unified description of both integer and fractional regimes within conventional quantum mechanics.

Related papers

• Real-time collisions of fractional charges in a trapped-ion Jackiw-Rebbi field theory [39.146761527401424]
  We study the effect of back-reaction and quantum fluctuations on the coupled dynamics of the full fermion-boson system.<n>Our results reveal how back-reaction and quantum fluctuations modify the stability and real-time evolution of fractionalized fermions.
  arXiv  Detail & Related papers  (2025-12-08T17:34:53Z)
• 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)
• Weak coupling limit for quantum systems with unbounded weakly commuting system operators [50.24983453990065]
  This work is devoted to a rigorous analysis of the weak coupling limit (WCL) for the reduced dynamics of an open infinite-dimensional quantum system interacting with electromagnetic field or a reservoir formed by Fermi or Bose particles.<n>We derive in the weak coupling limit the reservoir statistics, which is determined by whose terms in the multi-point correlation functions of the reservoir are non-zero in the WCL.<n>We prove that the resulting reduced system dynamics converges to unitary dynamics with a modified Hamiltonian which can be interpreted as a Lamb shift to the original Hamiltonian.
  arXiv  Detail & Related papers  (2025-05-13T05:32:34Z)
• Symmetries, Conservation Laws and Entanglement in Non-Hermitian Fermionic Lattices [37.69303106863453]
  Non-Hermitian quantum many-body systems feature steady-state entanglement transitions driven by unitary dynamics and dissipation.<n>We show that the steady state is obtained by filling single-particle right eigenstates with the largest imaginary part of the eigenvalue.<n>We illustrate these principles in the Hatano-Nelson model with periodic boundary conditions and the non-Hermitian Su-Schrieffer-Heeger model.
  arXiv  Detail & Related papers  (2025-04-11T14:06:05Z)
• Quantum work statistics across a critical point: full crossover from sudden quench to the adiabatic limit [27.336283729673195]
  Adiabatic and sudden-quench limits have been studied in detail, but the quantum work statistics along the crossover connecting these limits has largely been an open question.<n>Here we obtain exact scaling functions for the work statistics along the full crossover from adiabatic to sudden-quench limits for critical quantum impurity problems.<n>These predictions can be tested in charge-multichannel Kondo quantum dot devices, where the dissipated work corresponds to the creation of nontrivial excitations.
  arXiv  Detail & Related papers  (2025-02-03T18:36:07Z)
• Adiabatic State Preparation in a Quantum Ising Spin Chain [32.352947507436355]
  We report on adiabatic state preparation in the one-dimensional quantum Ising model using ultracold bosons in a tilted optical lattice. We observe enhanced fluctuations around the transition between paramagnetic and antiferromagnetic states, marking the precursor of quantum critical behavior.
  arXiv  Detail & Related papers  (2024-04-11T05:27:40Z)
• Quantum Reference Frames at the Boundary of Spacetime [0.0]
  An analysis is given of the local phase space of gravity coupled to matter to second order in perturbation theory. The boundary modes take the role of reference frames for both diffeomorphisms and internal Lorentz rotations. A multi-fingered Schr"odinger equation determines the relational evolution of the quantum states in the bulk.
  arXiv  Detail & Related papers  (2023-02-22T20:10:03Z)
• Anomalous localization and multifractality in a kicked quasicrystal [0.0]
  We report the experimental observation of multifractal matter and anomalous localization in a kicked Aubry-Andr'e-Harper quasicrystal. Our results open up the exploration of new states of matter characterized by an intricate interplay of fractal structure and quantum dynamics.
  arXiv  Detail & Related papers  (2022-03-17T17:02:53Z)
• 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)
• On quantum Hall effect, Kosterlitz-Thouless phase transition, Dirac magnetic monopole, and Bohr-Sommerfeld quantization [0.0]
  We address quantization phenomena in transport and vortex/precession-motion of low-dimensional systems. We discuss how the self-consistent Bohr-Sommerfeld quantization condition permeates the relationships between the quantization of integer Hall effect.
  arXiv  Detail & Related papers  (2020-09-16T17:57:14Z)
• Dynamical Mean-Field Theory for Markovian Open Quantum Many-Body Systems [0.0]
  We extend the nonequilibrium bosonic Dynamical Mean Field Theory to Markovian open quantum systems. As a first application, we address the steady-state of a driven-dissipative Bose-Hubbard model with two-body losses and incoherent pump.
  arXiv  Detail & Related papers  (2020-08-06T10:35:26Z)
• Unraveling the topology of dissipative quantum systems [58.720142291102135]
  We discuss topology in dissipative quantum systems from the perspective of quantum trajectories. We show for a broad family of translation-invariant collapse models that the set of dark state-inducing Hamiltonians imposes a nontrivial topological structure on the space of Hamiltonians.
  arXiv  Detail & Related papers  (2020-07-12T11:26:02Z)

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.