Numerical studies of the Pfaffian model of the ν = frac(5, 2) fractional quantum Hall effect

Csaba Toke; Nicolas Regnault; Jainendra K. Jain

doi:10.1016/j.ssc.2007.03.061

Numerical studies of the Pfaffian model of the ν = frac(5, 2) fractional quantum Hall effect

Csaba Toke, Nicolas Regnault, Jainendra K. Jain

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8 Scopus citations

Abstract

The Pfaffian model has been proposed for the fractional quantum Hall effect (FQHE) at ν = frac(5, 2). We examine it for the quasihole excitations by comparison with exact diagonalization results. Specifically, we consider the structure of the low-energy spectrum, accuracy of the microscopic wave functions, particle-hole symmetry, splitting of the degeneracies and off-diagonal long-range order. We also review how the 5/2 FQHE can be understood without appealing to the Pfaffian model. Implications for nonabelian braiding statistics will be mentioned.

Original language	English (US)
Pages (from-to)	504-511
Number of pages	8
Journal	Solid State Communications
Volume	144
Issue number	12
DOIs	https://doi.org/10.1016/j.ssc.2007.03.061
State	Published - Dec 2007

All Science Journal Classification (ASJC) codes

General Chemistry
Condensed Matter Physics
Materials Chemistry

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10.1016/j.ssc.2007.03.061

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title = "Numerical studies of the Pfaffian model of the ν = frac(5, 2) fractional quantum Hall effect",

abstract = "The Pfaffian model has been proposed for the fractional quantum Hall effect (FQHE) at ν = frac(5, 2). We examine it for the quasihole excitations by comparison with exact diagonalization results. Specifically, we consider the structure of the low-energy spectrum, accuracy of the microscopic wave functions, particle-hole symmetry, splitting of the degeneracies and off-diagonal long-range order. We also review how the 5/2 FQHE can be understood without appealing to the Pfaffian model. Implications for nonabelian braiding statistics will be mentioned.",

author = "Csaba Toke and Nicolas Regnault and Jain, {Jainendra K.}",

note = "Funding Information: We thank IDRIS-CNRS for a computer time allocation, the High Performance Computing (HPC) group at Penn State University ASET (Academic Services and Emerging Technologies) for assistance and computing time on the Lion-XL and Lion-XO clusters. Partial support of this research by the National Science Foundation is gratefully acknowledged.",

year = "2007",

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doi = "10.1016/j.ssc.2007.03.061",

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journal = "Solid State Communications",

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T1 - Numerical studies of the Pfaffian model of the ν = frac(5, 2) fractional quantum Hall effect

AU - Toke, Csaba

AU - Regnault, Nicolas

AU - Jain, Jainendra K.

N1 - Funding Information: We thank IDRIS-CNRS for a computer time allocation, the High Performance Computing (HPC) group at Penn State University ASET (Academic Services and Emerging Technologies) for assistance and computing time on the Lion-XL and Lion-XO clusters. Partial support of this research by the National Science Foundation is gratefully acknowledged.

PY - 2007/12

Y1 - 2007/12

N2 - The Pfaffian model has been proposed for the fractional quantum Hall effect (FQHE) at ν = frac(5, 2). We examine it for the quasihole excitations by comparison with exact diagonalization results. Specifically, we consider the structure of the low-energy spectrum, accuracy of the microscopic wave functions, particle-hole symmetry, splitting of the degeneracies and off-diagonal long-range order. We also review how the 5/2 FQHE can be understood without appealing to the Pfaffian model. Implications for nonabelian braiding statistics will be mentioned.

AB - The Pfaffian model has been proposed for the fractional quantum Hall effect (FQHE) at ν = frac(5, 2). We examine it for the quasihole excitations by comparison with exact diagonalization results. Specifically, we consider the structure of the low-energy spectrum, accuracy of the microscopic wave functions, particle-hole symmetry, splitting of the degeneracies and off-diagonal long-range order. We also review how the 5/2 FQHE can be understood without appealing to the Pfaffian model. Implications for nonabelian braiding statistics will be mentioned.

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Numerical studies of the Pfaffian model of the ν = frac(5, 2) fractional quantum Hall effect

Abstract

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