Anomalous fractional quantum Hall effect and multi-valued Hamiltonians
arXiv:2004.09135 · doi:10.1088/1361-648X/ac0bec
Abstract
We discuss anomalous fractional quantum Hall effect that exists without external magnetic field. We propose that excitations in such systems may be described effectively by non-interacting particles with the Hamiltonians defined on the Brillouin zone with a branch cut. Hall conductivity of such a system is expressed through the one-particle Green function. We demonstrate that for the Hamiltonians of the proposed type this expression takes fractional values times Klitzing constant. Possible relation of the proposed construction with degeneracy of ground state is discussed as well.
arXiv commentLatex, 14 pages, 4 figures
References in corpus (32)
- Topological Field Theory of Time-Reversal Invariant Insulators
- High temperature fractional quantum Hall states
- Fractional quantum Hall states at zero magnetic field
- Nearly-flat bands with nontrivial topology
- Fractional quantum Hall effect in the absence of Landau levels
- Interface engineering of quantum Hall effects in digital transition metal oxide heterostructures
- Fractional Quantum Hall Physics in Topological Flat Bands
- Fractional Quantum Hall States and Jack Polynomials
- Fractional Quantum Hall Effect of Hard-Core Bosons in Topological Flat Bands
- Flat Chern Band in a Two-Dimensional Organometallic Framework
- Topological Nematic States and Non-Abelian Lattice Dislocations
- Generic Wavefunction Description of Fractional Quantum Anomalous Hall States and Fractional Topological Insulators
- Realizing Fractional Chern Insulators with Dipolar Spins
- Quantum Mechanics in Phase Space
- Reaching Fractional Quantum Hall States with Optical Flux Lattices
- Position-Momentum Duality and Fractional Quantum Hall Effect in Chern Insulators
- Lectures on the Quantum Hall Effect
- Quantum Hall system in Tao-Thouless limit
- Geometrical engineering of a two-bands Chern insulator in two dimensions with arbitrary topological index
- Abelian and Non-abelian Hall Liquids and Charge Density Wave: Quantum Number Fractionalization in One and Two Dimensions
- Topological Flat Bands from Dipolar Spin Systems
- Fractional topological phases and broken time reversal symmetry in strained graphene
- Fractional quantum Hall states in lattices: Local models and physical implementation
- The Anatomy of Abelian and Non-Abelian Fractional Quantum Hall States
- Pseudopotential Formalism for Fractional Chern Insulators
- Topological bands with Chern number C=2 by dipolar exchange interactions
- Chern-Simons Composite Fermion Theory of Fractional Chern Insulators
- Hall conductivity as the topological invariant in phase space in the presence of interactions and non-uniform magnetic field
- Influence of interactions on the anomalous quantum Hall effect
- Crystal-symmetry preserving Wannier states for fractional chern insulators
- Optical lattice implementation scheme of a bosonic topological model with fermionic atoms
- Precise Wigner-Weyl calculus for lattice models