KohnSham Theory of the Fractional Quantum Hall Effect
Abstract
We formulate the KohnSham (KS) equations for the fractional quantum Hall effect by mapping the original electron problem into an auxiliary problem of composite fermions that experience a density dependent effective magnetic field. Selfconsistent solutions of the KS equations demonstrate that our formulation captures not only configurations with nonuniform densities but also topological properties such as fractional charge and fractional braid statistics for the quasiparticles excitations. Lastly, this method should enable a realistic modeling of the edge structure, the effect of disorder, spin physics, screening, and of fractional quantum Hall effect in mesoscopic devices.
 Authors:

 Pennsylvania State Univ., University Park, PA (United States). Dept. of Physics
 Publication Date:
 Research Org.:
 Pennsylvania State Univ., University Park, PA (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC), Basic Energy Sciences (BES)
 OSTI Identifier:
 1606393
 Grant/Contract Number:
 SC0005042
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Physical Review Letters
 Additional Journal Information:
 Journal Volume: 123; Journal Issue: 17; Journal ID: ISSN 00319007
 Publisher:
 American Physical Society (APS)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; Kohn Sham; Density Functional Theory; composite fermions
Citation Formats
Hu, Yayun, and Jain, J. K. KohnSham Theory of the Fractional Quantum Hall Effect. United States: N. p., 2019.
Web. doi:10.1103/PhysRevLett.123.176802.
Hu, Yayun, & Jain, J. K. KohnSham Theory of the Fractional Quantum Hall Effect. United States. https://doi.org/10.1103/PhysRevLett.123.176802
Hu, Yayun, and Jain, J. K. Fri .
"KohnSham Theory of the Fractional Quantum Hall Effect". United States. https://doi.org/10.1103/PhysRevLett.123.176802. https://www.osti.gov/servlets/purl/1606393.
@article{osti_1606393,
title = {KohnSham Theory of the Fractional Quantum Hall Effect},
author = {Hu, Yayun and Jain, J. K.},
abstractNote = {We formulate the KohnSham (KS) equations for the fractional quantum Hall effect by mapping the original electron problem into an auxiliary problem of composite fermions that experience a density dependent effective magnetic field. Selfconsistent solutions of the KS equations demonstrate that our formulation captures not only configurations with nonuniform densities but also topological properties such as fractional charge and fractional braid statistics for the quasiparticles excitations. Lastly, this method should enable a realistic modeling of the edge structure, the effect of disorder, spin physics, screening, and of fractional quantum Hall effect in mesoscopic devices.},
doi = {10.1103/PhysRevLett.123.176802},
journal = {Physical Review Letters},
number = 17,
volume = 123,
place = {United States},
year = {2019},
month = {10}
}
Web of Science
Figures / Tables:
Works referenced in this record:
HohenbergKohn theory including spin magnetism and magnetic fields
journal, January 2004
 Kohn, Walter; Savin, Andreas; Ullrich, Carsten A.
 International Journal of Quantum Chemistry, Vol. 100, Issue 1
TwoDimensional Magnetotransport in the Extreme Quantum Limit
journal, May 1982
 Tsui, D. C.; Stormer, H. L.; Gossard, A. C.
 Physical Review Letters, Vol. 48, Issue 22
Anomalous Quantum Hall Effect: An Incompressible Quantum Fluid with Fractionally Charged Excitations
journal, May 1983
 Laughlin, R. B.
 Physical Review Letters, Vol. 50, Issue 18
Generalized KohnSham schemes and the bandgap problem
journal, February 1996
 Seidl, A.; Görling, A.; Vogl, P.
 Physical Review B, Vol. 53, Issue 7
Composite Fermions in Quantum Dots
journal, February 1995
 Jain, J. K.; Kawamura, T.
 Europhysics Letters (EPL), Vol. 29, Issue 4
HohenbergKohn theory including spin magnetism and magnetic fields
journal, January 2004
 Kohn, Walter; Savin, Andreas; Ullrich, Carsten A.
 International Journal of Quantum Chemistry, Vol. 101, Issue 5
Aharonov–Bohm interference of fractional quantum Hall edge modes
journal, March 2019
 Nakamura, J.; Fallahi, S.; Sahasrabudhe, H.
 Nature Physics, Vol. 15, Issue 6
Statistics of Quasiparticles and the Hierarchy of Fractional Quantized Hall States
journal, April 1984
 Halperin, B. I.
 Physical Review Letters, Vol. 52, Issue 18
DensityFunctional Theory of the Fractional Quantum Hall Effect
journal, May 2017
 Zhao, Jianyun; Thakurathi, Manisha; Jain, Manish
 Physical Review Letters, Vol. 118, Issue 19
Orbitaldependent density functionals: Theory and applications
journal, January 2008
 Kümmel, Stephan; Kronik, Leeor
 Reviews of Modern Physics, Vol. 80, Issue 1
Density functionals for coulomb systems
journal, September 1983
 Lieb, Elliott H.
 International Journal of Quantum Chemistry, Vol. 24, Issue 3
Formation of an edge striped phase in the $\nu =\frac{1}{3}$ fractional quantum Hall system
journal, October 2001
 Tsiper, E. V.; Goldman, V. J.
 Physical Review B, Vol. 64, Issue 16
Universal variational functionals of electron densities, firstorder density matrices, and natural spinorbitals and solution of the vrepresentability problem
journal, December 1979
 Levy, M.
 Proceedings of the National Academy of Sciences, Vol. 76, Issue 12
Edge structure of fractional quantum Hall systems from densityfunctional theory
journal, December 1995
 Ferconi, M.; Geller, M. R.; Vignale, G.
 Physical Review B, Vol. 52, Issue 23
Berry phases for composite fermions: Effective magnetic field and fractional statistics
journal, September 2004
 Jeon, Gun Sang; Graham, Kenneth L.; Jain, Jainendra K.
 Physical Review B, Vol. 70, Issue 12
Statistics of Quasiparticles and the Hierarchy of Fractional Quantized Hall States
journal, June 1984
 Halperin, B. I.
 Physical Review Letters, Vol. 52, Issue 26
Ensemble Density Functional Theory of the Fractional Quantum Hall Effect
journal, November 1995
 Heinonen, O.; Lubin, M. I.; Johnson, M. D.
 Physical Review Letters, Vol. 75, Issue 22
Strong Correlation in KohnSham Density Functional Theory
journal, December 2012
 Malet, Francesc; GoriGiorgi, Paola
 Physical Review Letters, Vol. 109, Issue 24
Uniform magnetic fields in densityfunctional theory
journal, January 2018
 Tellgren, Erik I.; Laestadius, Andre; Helgaker, Trygve
 The Journal of Chemical Physics, Vol. 148, Issue 2
Fractional Statistics and the Quantum Hall Effect
journal, August 1984
 Arovas, Daniel; Schrieffer, J. R.; Wilczek, Frank
 Physical Review Letters, Vol. 53, Issue 7
Compositefermion approach for the fractional quantum Hall effect
journal, July 1989
 Jain, J. K.
 Physical Review Letters, Vol. 63, Issue 2
Constrained Density Functional Theory
journal, November 2011
 Kaduk, Benjamin; Kowalczyk, Tim; Van Voorhis, Troy
 Chemical Reviews, Vol. 112, Issue 1
Fractional Angular Momentum in ColdAtom Systems
journal, October 2014
 Zhang, Yuhe; Sreejith, G. J.; Gemelke, N. D.
 Physical Review Letters, Vol. 113, Issue 16
Some static and dynamical properties of a twodimensional Wigner crystal
journal, February 1977
 Bonsall, Lynn; Maradudin, A. A.
 Physical Review B, Vol. 15, Issue 4
Strong correlation in KohnSham density functional theory
text, January 2012
 Malet, Francesc; GoriGiorgi, Paola
 arXiv
The choice of basic variables in currentdensity functional theory
text, January 2012
 Tellgren, Erik I.; Kvaal, Simen; Sagvolden, Espen
 arXiv
Berry phases for composite fermions: effective magnetic field and fractional statistics
text, January 2004
 Jeon, Gun Sang; Graham, Kenneth L.; Jain, Jainendra K.
 arXiv
Ensemble density functional theory of the fractional quantum Hall effect
text, January 1995
 Heinonen, O.; Lubin, M. I.; Johnson, M. D.
 arXiv
Figures / Tables found in this record: