Band Structure of the Fractional Quantum Hall Effect

Abstract

The eigenstates of interacting electrons in the fractional quantum Hall phase typically form fairly well defined bands in the energy space. We show that the composite fermion theory gives insight into the origin of these bands and provides an accurate and complete microscopic description of the strongly correlated many-body states in the low-energy bands. Thus, somewhat like in Landau's fermi liquid theory, there is a one-to-one correspondence between the low energy Hilbert space of strongly interacting electrons in the fractinal quantum Hall regime and that of weakly interacting electrons in the integer quantum Hall regime.

10 pages

Cited by in corpus (91)

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• Fractional Quantum Hall Effect in Graphene: Quantitative Comparison between Theory and Experiment
• Structures for Interacting Composite Fermions: Stripes, Bubbles, and Fractional Quantum Hall Effect
• Luttinger theorem for the strongly correlated Fermi liquid of composite fermions
• Haldane fractional statistics in the fractional quantum Hall effect
• Entanglement entropy of the $\nu =1/2$ composite fermion non-Fermi liquid state
• State Counting for Excited Bands of the Fractional Quantum Hall Effect: Exclusion Rules for Bound Excitons
• Composite fermion theory of collective excitations in fractional quantum Hall effect
• Role of exciton screening in the 7/3 fractional quantum Hall effect
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• Phase Diagram of Fractional Quantum Hall Effect of Composite Fermions in Multi-Component Systems
• Fermi-sea-like correlations in a partially filled Landau level
• Skyrmions in the Fractional Quantum Hall Effect
• Spontaneous polarization of composite fermions in the $n=1$ Landau level of graphene
• Composite Fermions and Landau Level Mixing in the Fractional Quantum Hall Effect
• Unpaired composite fermion, topological exciton, and zero mode
• Fermi wave vector for the non-fully spin polarized composite-fermion Fermi sea
• Excitation Spectrum and Collective Modes of Composite Fermions
• Evidence of a fractional quantum Hall nematic phase in a microscopic model
• Composite-Fermion Picture for the Spin-Wave Excitation in the fractional quantum Hall system
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• Excitons of Composite Fermions
• Berry phases for composite fermions: effective magnetic field and fractional statistics
• Quench dynamics of collective modes in fractional quantum Hall bilayers
• A non-Abelian parton state for the $\nu =2+3/8$ fractional quantum Hall effect
• Multiple Magnetorotons and Spectral Sum Rules in Fractional Quantum Hall Systems
• Hierarchical structure in the orbital entanglement spectrum in Fractional Quantum Hall systems
• Quasiparticles and excitons for the Pfaffian quantum Hall state
• Exact results for model wave functions of anisotropic composite fermions in the fractional quantum Hall effect
• Spontaneous Magnetization of Composite Fermions
• Interplay between fractional quantum Hall liquid and crystal phases at low filling
• Hund's Rule for Composite Fermions
• Fractional Quantum Hall Effect in the Second Landau Level: the Importance of Inter-Composite-Fermion Interaction
• Positions of the magnetoroton minima in the fractional quantum Hall effect
• Composite Fermions on a Torus
• Higher Energy Composite Fermion Levels in the Fractional Quantum Hall Effect
• Unconventional ${\mathbb{Z}}_n$ parton states at $\nu =7/3$: The role of finite width
• Neutral Excitations of Quantum Hall States: a Density Matrix Renormalization Group Study
• Hamiltonian Description of Composite Fermions: Magnetoexciton Dispersions
• Partially spin polarized quantum Hall effect in the filling factor range 1/3 < nu < 2/5
• Fractional Quantum Hall States in Low-Zeeman-Energy Limit
• Abelian parton state for the $\nu =4/11$ fractional quantum Hall effect
• Microscopic Study of Edge Excitations of Spin-Polarized and Spin-Unpolarized $\nu =2/3$ Fractional Quantum Hall Effect
• Observation of non-conventional spin waves in composite fermion ferromagnets
• Energy gaps and roton structure above the nu=1/2 Laughlin state of a rotating dilute Bose-Einstein condensate
• Composite Fermion states on the torus
• Search for exact local Hamiltonians for general fractional quantum Hall states
• Hamiltonian Description of Composite Fermions: Calculation of Gaps
• Particle-hole symmetry for composite fermions: An emergent symmetry in the fractional quantum Hall effect
• Fractional quantum Hall effect arising from repulsive three body interaction
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• Neutral Collective Modes in Spin-Polarized Fractional Quantum Hall States at Filling Factors 1/3, 2/5, 3/7, and 4/9
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• Haldane's Fractional Statistics and the Riemann-Roch Theorem
• Half-Integral Spin-Singlet Quantum Hall Effect
• Theory of anyon excitons: Relation to excitons of nu=1/3 and nu=2/3 incompressible liquids
• Girvin-MacDonald-Platzman Collective Mode at General Filling Factors: Magneto-Roton Minimum at Half-Filled Landau Level
• Berry phase of the composite-fermion Fermi Sea: Effect of Landau-level mixing
• A First-Landau-Level Laughlin/Jain Wave Function for the Fractional Quantum Hall Effect
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• Fractional quantum Hall effect in higher Landau levels
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• Anomalously low magnetoroton energies of the unconventional fractional quantum Hall states of composite fermions
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• Composite-Fermion Analysis of the Double-Layer Fractional Quantum Hall System
• Electrons in a Strong Magnetic Field on a Disk
• Compressible $\nu =\frac{1}{2}$ state in a finite size study?
• Moiré Assisted Fractional Quantum Hall State Spectroscopy
• Static structure factor and the dispersion of the Girvin-MacDonald-Platzman density mode for fractional quantum Hall fluids on the Haldane sphere
• Unlocking new regimes in fractional quantum Hall effect with quaternions
• Roton minimum at $\nu =1/2$ filled fractional quantum Hall effect of Bose particles
• Haldane's Fractional Statistics and the Lowest Landau Level on a Torus
• On the modular covariance properties of composite fermions on the torus
• Collective excitations of quantum Hall states under tilted magnetic field
• Composite fermions in the neighborhood of $\nu =1/3$
• Dispersion of neutral collective modes in partonic fractional quantum Hall states and its applications to paired states of composite fermions
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• Composite fermion basis for two-component Bose gases
• Dispersion of collective modes in spinful fractional quantum Hall states on the sphere
• Crossover from Integer to Fractional Quantum Hall Effect
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