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

arXiv:hep-th/9307132 · Modern Physics Letters A

LARGE-N COLLECTIVE FIELD THEORY APPLIED TO ANYONS IN MAGNETIC FIELDS

Hideaki Hiro-Oka, Hisakazu Minakata

Published Dec 7, 1993• 3 citations
arXivHTMLPDF

Abstract

We present a large-N collective field formalism for anyons in external magnetic fields interacting with an arbitrary two-body potential. We discuss how the Landau levels are reproduced in our framework. We apply it to the soluble model for anyons proposed by Girvin et al., and obtain the dispersion relation of the collective modes for arbitrary statistical parameters.

DOI
10.1142/s0217732393002282

Related papers

ANYONS IN A MAGNETIC FIELD: LANDAU LEVELS AND VERTEX OPERATOR REPRESENTATION

Gerald V. Dunne, Alberto Lerda A, Carlo A. Trugenberger

We construct exact many-body eigenstates of both energy and angular momentum for the N-anyon problem in an external magnetic field. Such states span the full ground-state eigenspace and have a natural representation in terms of the Fubini-Veneziano vertex operators of string theory.

International Journal of Modern Physics B•Jun 1, 1991•18 citations

GROUND STATE OF N HARMONICALLY BOUND ANYONS IN A MAGNETIC FIELD

R. Chitra

The properties of the ground state of N anyons in an external magnetic field and a harmonic oscillator potential are computed in the large-N limit using the Thomas-Fermi approximation. The number of level crossings in the ground state as a function of the harmonic frequency, the strength and the direction of the magnetic field and N are also studied.

Modern Physics Letters A•Dec 14, 1992•0 citations

MEAN FIELD APPROXIMATION FOR ANYONS IN A MAGNETIC FIELD

E. Westerberg

The mean field equations for anyons in an external homogeneous magnetic field are studied and two classes of mean field solutions are explicitly constructed. The first class of solutions, corresponding to one filled Landau level in the combined external and smeared out statistical magnetic fields, is compared to the corresponding exact groundstate solutions. The energies are found to agree well at low densities and when the statistical field is not too strong compared to the background field. At high densities the fermi pressure increases the mean field energy indefinitely. The mean field solutions also miss the lower part of the energy spectrum. To the second class of mean field solutions no corresponding anyon state is known. These solutions represent the anyonic continuation of the fermi state with two filled Landau levels.

International Journal of Modern Physics B•May 15, 1993•7 citations

LANDAU LEVELS AND VERTEX OPERATIONS FOR ANYONS

Gerald V. Dunne, Alberto Lerda A, Carlo A. Trugenberger

We construct exact many-body eigenstates of both energy and angular momentum for the N-anyon problem in an external magnetic field. We show that such states span the full ground state eigenspace and arise as correlation functions of Fubini-Veneziano vertex operators of string theory.

Modern Physics Letters A•Sep 28, 1991•30 citations

MULTI-ANYONS IN THE MAGNETIC FIELD

Taeseung Choi, Jungjai Lee, Chang‐Mo Ryu

We consider the external magnetic field effects on the two types of anyons with fractional statistical parameter p/q with coprimes p and q, one with a fractional charge e/q and the other with a fractional flux p ϕ0/q by exact ground state wave function. We also study the geometry in which a two-dimensional strip of anyons contains an island of anyons with different statistical parameters in their equilibrium. The equilibrium inside an island is shown to be periodic with respect to the magnetic flux through the island. The period for the fractional charge anyon equals to the integer multiple of the fundamental flux quantum. On the other hand, in the case of the fractional flux anyon, the period is found to be the fractional multiple of the fundamental flux quantum.

arXiv:cond-mat/9802272•Modern Physics Letters B•Nov 10, 1999•1 citation

AVERAGE FIELD APPROXIMATION FOR ALMOST BOSONIC ANYONS IN A MAGNETIC FIELD

Théotime Girardot

We study the ground state of a large number N of 2D anyons in an external magnetic field. We consider a scaling limit where the statistics parameter α tends to zero when N tends to infinity which allows the statistics to be seen as a "perturbation from the bosonic end". Our model is that of bosons in a magnetic field and interacting through long-range magnetic potential generated by magnetic charges carried by each particle, smeared over discs of radius R. Our method allows to take R tends to not too fast at the same time as N tends to infinity. We use the information theoretic version of the de Finetti theorem of Brandão and Harrow to justify the so-called "average field approximation": the particles behave like independent, identically distributed bosons interacting via a self-consistent magnetic field.

•Oct 18, 2019•14 citations
We present a large-N collective field formalism for anyons in external magnetic fields interacting with an arbitrary two-body potential. We discuss how the Landau levels are reproduced in our framework. We apply it to the soluble model for anyons proposed by Girvin et al., and obtain the dispersion relation of the collective modes for arbitrary statistical parameters.
The mean field equations for anyons in an external homogeneous magnetic field are studied and two classes of mean field solutions are explicitly constructed. The first class of solutions, corresponding to one filled Landau level in the combined external and smeared out statistical magnetic fields, is compared to the corresponding exact groundstate solutions. The energies are found to agree well at low densities and when the statistical field is not too strong compared to the background field. At high densities the fermi pressure increases the mean field energy indefinitely. The mean field solutions also miss the lower part of the energy spectrum. To the second class of mean field solutions no corresponding anyon state is known. These solutions represent the anyonic continuation of the fermi state with two filled Landau levels.
We consider the external magnetic field effects on the two types of anyons with fractional statistical parameter p/q with coprimes p and q, one with a fractional charge e/q and the other with a fractional flux p ϕ0/q by exact ground state wave function. We also study the geometry in which a two-dimensional strip of anyons contains an island of anyons with different statistical parameters in their equilibrium. The equilibrium inside an island is shown to be periodic with respect to the magnetic flux through the island. The period for the fractional charge anyon equals to the integer multiple of the fundamental flux quantum. On the other hand, in the case of the fractional flux anyon, the period is found to be the fractional multiple of the fundamental flux quantum.
We study the ground state of a large number N of 2D anyons in an external magnetic field. We consider a scaling limit where the statistics parameter α tends to zero when N tends to infinity which allows the statistics to be seen as a "perturbation from the bosonic end". Our model is that of bosons in a magnetic field and interacting through long-range magnetic potential generated by magnetic charges carried by each particle, smeared over discs of radius R. Our method allows to take R tends to not too fast at the same time as N tends to infinity. We use the information theoretic version of the de Finetti theorem of Brandão and Harrow to justify the so-called "average field approximation": the particles behave like independent, identically distributed bosons interacting via a self-consistent magnetic field.