Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

International Journal of Modern Physics B

CURRENT OPERATORS IN THE LOWEST LANDAU LEVEL

JUAN MARTÍNEZ, Michael Stone

Published Nov 30, 1993• 42 citations
Publisher

Abstract

We use Noether’s theorem to generate a consistent definition of the current operator for electrons restricted to the lowest Landau level. We exhibit the connection between this current and the Moyal bracket, or W∞, algebra, and use it to derive the edge-charge algebra for the ν=1/(2n+1) FQHE states.
DOI
10.1142/s0217979293003723

Related papers

VERTEX OPERATORS IN THE QUANTUM HALL EFFECT

Michael Stone

The edge states of the quantum Hall effect carry representations of chiral current algebras and their associated groups. In the simplest case of a single filled Landau level, I demonstrate explicitly how the group action affects the many-body states, and why the Kac-Peterson cocycle appears in the group multiplication law. I show how these representations may be used to construct vertex operators which create localised edge excitations, and indicate how they are related to the bulk quasi-particles.

International Journal of Modern Physics B•Feb 10, 1991•50 citations

THE HYDRODYNAMICAL LIMIT OF QUANTUM HALL SYSTEM

D. SREEDHAR BABU, R. SHANKAR, M. SIVAKUMAR

We study the current algebra of FQHE systems in the hydrodynamical limit of small amplitude, long-wavelength fluctuations. We show that the algebra simplifies considerably in this limit. The Hamiltonian is expressed in a current–current form and the operators creating inter-Landau level and lowest Landau level collective excitations are identified.

arXiv:cond-mat/0107270•International Journal of Modern Physics B•Aug 10, 2001•1 citation

Charge and current in the quantum Hall matrix model

T. H. Hansson, Janik Kailasvuori, A. Karlhede

We extend the quantum Hall matrix model to include couplings to external electric and magnetic fields. The associated current suffers from matrix ordering ambiguities even in the classical model. We calculate the linear response at low momenta---this is unambigously defined. In particular, we obtain the correct fractional quantum Hall conductivity, and the expected density modulations in response to a weak and slowly varying magnetic field. In the quantum theory the ordering ambiguities are more severe, but we are able to construct a good density operator, satisfying the pertinent lowest Landau level commutator algebra, for the special case of $2\ifmmode\times\else\texttimes\fi{}2$ matrices. Our results support the conjecture that the quantum Hall matrix models do describe important aspects of the dynamics of electrons in the lowest Landau level.

arXiv:cond-mat/0304271•Physical review. B, Condensed matter•Jul 29, 2003•19 citations

EFFECTIVE INTERACTIONS OF PLANAR FERMIONS IN A STRONG MAGNETIC FIELD-THE EFFECT OF LANDAU LEVEL MIXING

Rashmi Ray, G. Gat

We obtain expressions for the current operator in the lowest Landau level (L.L.L.) field theory, where higher Landau level mixing due to various external and interparticle interactions is sytematically taken into account. We consider the current operators in the presence of electromagnetic interactions, both Coulomb and time-dependent, as well as local four-fermi interactions. The importance of Landau level mixing for long-range interactions is especially emphasized. We also calculate the edge-current for a finite sample.

•Jan 1, 1994•1 citation

Approximate representations of a local current algebra

Ralph Menikoff, David H. Sharp

An approximate method for dealing with nonrelativistic many-body quantum systems having short range interactions is developed using local currents. The scheme is based on determining approximate representations of subalgebras of the local currents. This mathematical framework is used to discuss several approximation schemes.

Journal of Mathematical Physics•Dec 1, 1975•3 citations

Exactly Solvable Model for Strongly Interacting Electrons in a Magnetic Field

Abhishek Anand, Jainendra K. Jain, G. J. Sreejith

States of strongly interacting particles are of fundamental interest in physics and can produce exotic emergent phenomena and topological structures. We consider here two-dimensional electrons in a magnetic field, and, departing from the standard practice of restricting to the lowest LL, introduce a model short-range interaction that is infinitely strong compared to the cyclotron energy. We demonstrate that this model lends itself to an exact solution for the ground as well as excited states at arbitrary filling factors ν<1/2p and produces a fractional quantum Hall effect at fractions of the form ν=n/(2pn+1), where n and p are integers. The fractional quantum Hall states of our model share many topological properties with the corresponding Coulomb ground states in the lowest Landau level, such as the edge physics and the fractional charge of the excitations.

arXiv:2010.12594•Physical Review Letters•Mar 29, 2021•6 citations
The edge states of the quantum Hall effect carry representations of chiral current algebras and their associated groups. In the simplest case of a single filled Landau level, I demonstrate explicitly how the group action affects the many-body states, and why the Kac-Peterson cocycle appears in the group multiplication law. I show how these representations may be used to construct vertex operators which create localised edge excitations, and indicate how they are related to the bulk quasi-particles.
We extend the quantum Hall matrix model to include couplings to external electric and magnetic fields. The associated current suffers from matrix ordering ambiguities even in the classical model. We calculate the linear response at low momenta---this is unambigously defined. In particular, we obtain the correct fractional quantum Hall conductivity, and the expected density modulations in response to a weak and slowly varying magnetic field. In the quantum theory the ordering ambiguities are more severe, but we are able to construct a good density operator, satisfying the pertinent lowest Landau level commutator algebra, for the special case of $2\ifmmode\times\else\texttimes\fi{}2$ matrices. Our results support the conjecture that the quantum Hall matrix models do describe important aspects of the dynamics of electrons in the lowest Landau level.
We obtain expressions for the current operator in the lowest Landau level (L.L.L.) field theory, where higher Landau level mixing due to various external and interparticle interactions is sytematically taken into account. We consider the current operators in the presence of electromagnetic interactions, both Coulomb and time-dependent, as well as local four-fermi interactions. The importance of Landau level mixing for long-range interactions is especially emphasized. We also calculate the edge-current for a finite sample.
States of strongly interacting particles are of fundamental interest in physics and can produce exotic emergent phenomena and topological structures. We consider here two-dimensional electrons in a magnetic field, and, departing from the standard practice of restricting to the lowest LL, introduce a model short-range interaction that is infinitely strong compared to the cyclotron energy. We demonstrate that this model lends itself to an exact solution for the ground as well as excited states at arbitrary filling factors ν<1/2p and produces a fractional quantum Hall effect at fractions of the form ν=n/(2pn+1), where n and p are integers. The fractional quantum Hall states of our model share many topological properties with the corresponding Coulomb ground states in the lowest Landau level, such as the edge physics and the fractional charge of the excitations.