skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Algebraic approach to fractional quantum Hall effect

Abstract

We construct an algebraic description for the ground state and for the static response of the quantum Hall plateaus with a filling factor ν = N/(2N + 1) in the large N limit. Here, by analyzing the algebra of the fluctuations of the shape of the Fermi surface of the composite fermions, we find the explicit form of the projected static structure (SSF) factor at large N and fixed z = (2N + 1)qℓ B ~ 1, where q is the wave number at which the system is probed, and ℓ B is the magnetic length. When z < 3.8, we obtain the exact universal formula for the projected SSF. The formula does not depend on the particular form of the Hamiltonian.

Authors:
 [1];  [2]
  1. Oxford Univ. (United Kingdom)
  2. Univ. of Chicago, IL (United States)
Publication Date:
Research Org.:
Univ. of Chicago, IL (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)
OSTI Identifier:
1594024
Alternate Identifier(s):
OSTI ID: 1488626
Grant/Contract Number:  
SC0009924; FG02-13ER41958
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review B
Additional Journal Information:
Journal Volume: 98; Journal Issue: 24; Journal ID: ISSN 2469-9950
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; Fractional quantum Hall effect; Bosonization; Fermi liquid theory

Citation Formats

Nguyen, Dung Xuan, and Son, Dam Thanh. Algebraic approach to fractional quantum Hall effect. United States: N. p., 2018. Web. doi:10.1103/PhysRevB.98.241110.
Nguyen, Dung Xuan, & Son, Dam Thanh. Algebraic approach to fractional quantum Hall effect. United States. doi:10.1103/PhysRevB.98.241110.
Nguyen, Dung Xuan, and Son, Dam Thanh. Sat . "Algebraic approach to fractional quantum Hall effect". United States. doi:10.1103/PhysRevB.98.241110. https://www.osti.gov/servlets/purl/1594024.
@article{osti_1594024,
title = {Algebraic approach to fractional quantum Hall effect},
author = {Nguyen, Dung Xuan and Son, Dam Thanh},
abstractNote = {We construct an algebraic description for the ground state and for the static response of the quantum Hall plateaus with a filling factor ν = N/(2N + 1) in the large N limit. Here, by analyzing the algebra of the fluctuations of the shape of the Fermi surface of the composite fermions, we find the explicit form of the projected static structure (SSF) factor at large N and fixed z = (2N + 1)qℓB ~ 1, where q is the wave number at which the system is probed, and ℓB is the magnetic length. When z < 3.8, we obtain the exact universal formula for the projected SSF. The formula does not depend on the particular form of the Hamiltonian.},
doi = {10.1103/PhysRevB.98.241110},
journal = {Physical Review B},
number = 24,
volume = 98,
place = {United States},
year = {2018},
month = {12}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 2 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

Two-Dimensional Magnetotransport in the Extreme Quantum Limit
journal, May 1982


Is the Composite Fermion a Dirac Particle?
journal, September 2015


Hall Viscosity and Electromagnetic Response
journal, February 2012


Particle-hole symmetry and composite fermions in fractional quantum Hall states
journal, May 2018


Anomalous Quantum Hall Effect: An Incompressible Quantum Fluid with Fractionally Charged Excitations
journal, May 1983


Bimetric Theory of Fractional Quantum Hall States
journal, November 2017


Microscopic theory of the fractional quantum Hall effect
journal, April 1992


Framing Anomaly in the Effective Theory of the Fractional Quantum Hall Effect
journal, January 2015


Dual Dirac Liquid on the Surface of the Electron Topological Insulator
journal, November 2015


Geometry of quantum Hall states: Gravitational anomaly and transport coefficients
journal, November 2015


Effective-Field-Theory Model for the Fractional Quantum Hall Effect
journal, January 1989


Anomalous dynamical scaling from nematic and U(1) gauge field fluctuations in two-dimensional metals
journal, July 2015


Particle-Hole Duality in the Lowest Landau Level
journal, May 2017


Fractional quantum Hall systems near nematicity: Bimetric theory, composite fermions, and Dirac brackets
journal, May 2018


Magneto-roton theory of collective excitations in the fractional quantum Hall effect
journal, February 1986


Theory of the half-filled Landau level
journal, March 1993


Fermi wave vector for the partially spin-polarized composite-fermion Fermi sea
journal, December 2017


Fractional Quantum Hall Effect in a Curved Space: Gravitational Anomaly and Electromagnetic Response
journal, July 2014


Geometrical Description of the Fractional Quantum Hall Effect
journal, September 2011


Higher-Spin Theory of the Magnetorotons
journal, November 2016


Fractional quantum Hall effect and Chern-Simons gauge theories
journal, September 1991


Shift and Spin Vector: New Topological Quantum Numbers for the Hall Fluids
journal, November 1992


Conformal invariance of chiral edge theories
journal, June 2009


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


Erratum: Framing Anomaly in the Effective Theory of the Fractional Quantum Hall Effect [Phys. Rev. Lett. 114 , 016805 (2015)]
journal, April 2015


Quantum phase transitions of metals in two spatial dimensions. I. Ising-nematic order
journal, August 2010