Adiabatic construction of hierarchical quantum Hall states

Greiter, Martin; Wilczek, Frank

doi:10.1103/physrevb.104.l121111

Title: Adiabatic construction of hierarchical quantum Hall states

Abstract

We propose an exact model of anyon ground states including higher Landau levels, and use it to obtain fractionally quantized Hall states at filling fractions ν = p/(p(m - 1) + 1) with m odd, from integer Hall states at ν = p through adiabatic localization of magnetic flux. For appropriately chosen two-body potential interactions, the energy gap remains intact during the process. The construction hence establishes the existence of incompressible states at these fillings.

Authors:

^[1];

^[2]

Univ. of Wurzburg (Germany)
Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States); Shanghai Jiao Tong Univ. (China); Arizona State Univ., Tempe, AZ (United States); Stockholm Univ. (Sweden)

Publication Date:: Wed Sep 01 00:00:00 EDT 2021

Research Org.:: Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

Sponsoring Org.:: USDOE Office of Science (SC); German Research Foundation (DFG); European Research Council (ERC); Swedish Research Council (SRC)

OSTI Identifier:: 1851680

Grant/Contract Number:: SC0012567; 258499086; GR-1715/3-1; 742104; 335-2014-7424

Resource Type:: Accepted Manuscript

Journal Name:: Physical Review. B

Additional Journal Information:: Journal Volume: 104; Journal Issue: 12; Journal ID: ISSN 2469-9950

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 36 MATERIALS SCIENCE; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Anyons; Composite fermions; Fractional quantum Hall effect

Citation Formats


                    Greiter, Martin, and Wilczek, Frank. Adiabatic construction of hierarchical quantum Hall states.  United States: N. p., 2021. 
Web.  doi:10.1103/physrevb.104.l121111.

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                    Greiter, Martin, & Wilczek, Frank. Adiabatic construction of hierarchical quantum Hall states.  United States.  https://doi.org/10.1103/physrevb.104.l121111

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                    Greiter, Martin, and Wilczek, Frank. Wed .  
"Adiabatic construction of hierarchical quantum Hall states".  United States.  https://doi.org/10.1103/physrevb.104.l121111.  https://www.osti.gov/servlets/purl/1851680.

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@article{osti_1851680,

  title        = {Adiabatic construction of hierarchical quantum Hall states},

  author       = {Greiter, Martin and Wilczek, Frank},

  abstractNote = {We propose an exact model of anyon ground states including higher Landau levels, and use it to obtain fractionally quantized Hall states at filling fractions ν = p/(p(m - 1) + 1) with m odd, from integer Hall states at ν = p through adiabatic localization of magnetic flux. For appropriately chosen two-body potential interactions, the energy gap remains intact during the process. The construction hence establishes the existence of incompressible states at these fillings.},

  doi          = {10.1103/physrevb.104.l121111},

  journal      = {Physical Review. B},

  number       = 12,

  volume       = 104,

  place        = {United States},

  year         = {Wed Sep 01 00:00:00 EDT 2021},

  month        = {Wed Sep 01 00:00:00 EDT 2021}

}

Copy to clipboard

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Title: Adiabatic construction of hierarchical quantum Hall states

Abstract

Citation Formats

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Anyons in a magnetic field journal, April 1990

Statistics of Quasiparticles and the Hierarchy of Fractional Quantized Hall States journal, April 1984

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Fractional Quantization of the Hall Effect: A Hierarchy of Incompressible Quantum Fluid States journal, August 1983

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Jain-2/5 parent Hamiltonian: Structure of zero modes, dominance patterns, and zero mode generators journal, May 2017

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Order Parameter and Ginzburg-Landau Theory for the Fractional Quantum Hall Effect journal, January 1989

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Heuristic Principle for Quantized hall States journal, September 1990

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Nonabelions in the fractional quantum hall effect journal, August 1991

Hierarchical Nature of the Quantum Hall Effects journal, February 2012

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Non-Abelian Statistics of Half-Quantum Vortices in p -Wave Superconductors journal, January 2001

Exactly soluble model of fractional statistics journal, September 1990

Off-diagonal long-range order, oblique confinement, and the fractional quantum Hall effect journal, March 1987

On Singular Anyon Wavefunctions journal, March 1991

Topological Orders in Rigid States journal, February 1990

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Composite Fermions in the Hilbert Space of the Lowest Electronic Landau Level journal, September 1997

Composite anyons on a torus journal, September 2021

Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries and the fractional quantum Hall effect journal, April 2000

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Exact results for the fractional quantum Hall effect with general interactions journal, April 1985

Composite-fermion approach for the fractional quantum Hall effect journal, July 1989

Scaling theory of the fractional quantum Hall effect journal, March 1990

Is the Composite Fermion a Dirac Particle?
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Prediction of a Non-Abelian Fractional Quantum Hall State with $f$ -Wave Pairing of Composite Fermions in Wide Quantum Wells
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Local Two-Body Parent Hamiltonians for the Entire Jain Sequence
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Origin of the ν=2/5 fractional quantum Hall effect
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Anyons in a magnetic field
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Statistics of Quasiparticles and the Hierarchy of Fractional Quantized Hall States
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Paired Hall state at half filling
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Fractional Quantization of the Hall Effect: A Hierarchy of Incompressible Quantum Fluid States
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Magnetic Flux, Angular Momentum, and Statistics
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Order Parameter and Ginzburg-Landau Theory for the Fractional Quantum Hall Effect
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Entangled Pauli principles: The DNA of quantum Hall fluids
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Landau Level Mixing and the Ground State of the $ν = 5 / 2$ Quantum Hall Effect
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Fractional Statistics and the Quantum Hall Effect
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Microscopic formulation of the hierarchy of quantized Hall states
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Fractional statistics on a torus
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Microscopic derivation of Ginzburg-Landau theories for hierarchical quantum Hall states
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Composite-fermion wave functions as correlators in conformal field theory
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Nonabelions in the fractional quantum hall effect
journal, August 1991

Hierarchical Nature of the Quantum Hall Effects
journal, February 2012

Anomalous Quantum Hall Effect: An Incompressible Quantum Fluid with Fractionally Charged Excitations
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Paired Hall states
journal, May 1992

Even denominator fractional quantum Hall states in higher Landau levels of graphene
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Non-Abelian Statistics of Half-Quantum Vortices in $p$ -Wave Superconductors
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Exactly soluble model of fractional statistics
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Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries and the fractional quantum Hall effect
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Scaling theory of the fractional quantum Hall effect
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