scholarly journals NONCOMMUTATIVE FIELD THEORY AND THE DYNAMICS OF QUANTUM HALL FLUIDS

2002 ◽  
Vol 17 (25) ◽  
pp. 3589-3606 ◽  
Author(s):  
J. L. F. BARBÓN ◽  
A. PAREDES
Keyword(s):  
Field Theory ◽  
Spatial Structure ◽  
Effective Action ◽  
Quantum Hall ◽  
Weak Field ◽  
Density Fluctuations ◽  
Wigner Crystal ◽  
Vertex Operators ◽  
Noncommutative Field Theory ◽  
Chern Simons

We study the spectrum of density fluctuations of fractional Hall fluids in the context of the noncommutative hydrodynamical model of Susskind. We show that, within the weak-field expansion, the leading correction to the noncommutative Chern–Simons Lagrangian (a Maxwell term in the effective action), destroys the incompressibility of the Hall fluid due to strong UV/IR effects at one loop. We speculate on possible relations of this instability with the transition to the Wigner crystal, and conclude that calculations within the weak-field expansion must be carried out with an explicit ultraviolet cutoff at the noncommutativity scale. We point out that the noncommutative dipoles exactly match the spatial structure of the Halperin–Kallin quasiexcitons. Therefore, we propose that the noncommutative formalism must describe accurately the spectrum at very large momenta, provided no weak-field approximations are made. We further conjecture that the noncommutative open Wilson lines are "vertex operators" for the quasiexcitons.

scholarly journals A Chern-Simons effective field theory for the Pfaffian quantum Hall state

1998 ◽  
Vol 516 (3) ◽  
pp. 704-718 ◽  
Author(s):  
Eduardo Fradkin ◽  
Chetan Nayak ◽  
Alexei Tsvelik ◽  
Frank Wilczek
Keyword(s):  
Field Theory ◽  
Effective Field Theory ◽  
Quantum Hall ◽  
Effective Field ◽  
Chern Simons ◽  
Quantum Hall State

CONNECTIONS BETWEEN THE QUANTUM HALL EFFECT AND CONFORMAL FIELD THEORY

1992 ◽  
Vol 07 (30) ◽  
pp. 2837-2849
Author(s):  
GREG NAGAO ◽  
QIAN NIU ◽  
JOSÉ GAITE
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Effective Field ◽  
Vertex Operators ◽  
Effective Hamiltonian ◽  
Cyclotron Motion ◽  
Conformal Field

The quantum Hall effect (QHE) is studied in the context of a conformal field theory (CFT). Winding state vertex operators for an effective field of N "spins" associated with the cyclotron motion of particles are defined. The effective field of spins may be used to define an effective Hamiltonian. This effective Hamiltonian describes the collective motion of the N particles (with coupling κ0) together with a current-current interaction (of strength κ1). Such a system gives rise to a CFT in the large-N limit when κ0=κ1. The Laughlin wave function is derived from this CFT as an N'-point correlation function of winding state vertex operators.

TWISTED SYMMETRY AND NONCOMMUTATIVE FIELD THEORY

2012 ◽  
Vol 13 ◽  
pp. 54-65
Author(s):  
MARIJA DIMITRIJEVIĆ ◽  
LARISA JONKE
Keyword(s):  
Field Theory ◽  
Effective Action ◽  
Degrees Of Freedom ◽  
Deformation Parameter ◽  
Field Theories ◽  
Gauge Field Theory ◽  
Noncommutative Field Theory ◽  
First Order ◽  
Minkowski Space Time ◽  
Noncommutative Spaces

Although the meaning of twisted symmetry is still not fully understood, the twist approach has its advantages in the construction of field theories on noncommutative spaces. We discuss these advantages on the example of κ-Minkowski space-time. We construct the noncommutative U(1) gauge field theory. Especially the action is written as an integral of a maximal form, thus solving the cyclicity problem of the integral in κ-Minkowski. Using the Seiberg-Witten map to relate noncommutative and commutative degrees of freedom the effective action with the first order corrections in the deformation parameter is obtained.

scholarly journals CHERN-SIMONS DUALITY AND THE QUANTUM HALL EFFECT

1996 ◽  
Vol 11 (19) ◽  
pp. 3587-3608 ◽  
Author(s):  
A.P. BALACHANDRAN ◽  
L. CHANDAR ◽  
B. SATHIAPALAN
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Duality Transformation ◽  
Scalar Field Theory ◽  
Anomaly Cancellation ◽  
Duality Transformations ◽  
Chern Simons

In previous work on the quantum Hall effect on an annulus, we used O(d, d; Z) duality transformations on the action describing edge excitations to generate the Haldane hierarchy of Hall conductivities. Here we generate the corresponding hierarchy of “bulk actions” which are associated with Chern-Simons (CS) theories, the connection between the bulk and edge arising from the requirement of anomaly cancellation. We also find a duality transformation for the CS theory exactly analogous to the [Formula: see text] duality of the scalar field theory at the edge.

scholarly journals Quantum Hall physics = noncommutative field theory

2001 ◽  
Vol 2001 (10) ◽  
pp. 039-039 ◽  
Author(s):  
Simeon Hellerman ◽  
Mark Van Raamsdonk
Keyword(s):  
Field Theory ◽  
Quantum Hall ◽  
Noncommutative Field Theory

scholarly journals Noncommutative field theory description of quantum Hall Skyrmions

2001 ◽  
Vol 64 (8) ◽  
Author(s):  
Bum-Hoon Lee ◽  
Kyungsun Moon ◽  
Chaiho Rim
Keyword(s):  
Field Theory ◽  
Quantum Hall ◽  
Noncommutative Field Theory

THE QUANTUM HALL EFFECT AT ARBITRARY RATIONAL FILLING: A PROPOSAL

1992 ◽  
Vol 07 (28) ◽  
pp. 2583-2591 ◽  
Author(s):  
G. CRISTOFANO ◽  
G. MAIELLA ◽  
R. MUSTO ◽  
F. NICODEMI
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Hall Effect ◽  
Quantum Hall Effect ◽  
Hierarchical Model ◽  
Quantum Hall ◽  
Coulomb Gas ◽  
Vertex Operators ◽  
Two Dimensional ◽  
Conformal Field

A description of the quantum Hall effect, already proposed for the fractional filling ν=1/m, based on the introduction of Coulomb gas-like vertex operators typical of a two-dimensional conformal field theory, is extended to the case ν=p/m. The resulting physical picture is compared with the hierarchical model.

scholarly journals W-infinity symmetry in the quantum hall effect beyond the edge

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Andrea Cappelli ◽  
Lorenzo Maffi
Keyword(s):  
Field Theory ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Incompressible Fluids ◽  
Density Fluctuations ◽  
Finite Limit ◽  
Theory Approach ◽  
Conformal Field ◽  
Edge Reconstruction ◽  
Laughlin States

Abstract The description of chiral quantum incompressible fluids by the W∞ symmetry can be extended from the edge, where it encompasses the conformal field theory approach, to the non-conformal bulk. The two regimes are characterized by excitations with different sizes, energies and momenta within the disk geometry. In particular, the bulk quantities have a finite limit for large droplets. We obtain analytic results for the radial shape of excitations, the edge reconstruction phenomenon and the energy spectrum of density fluctuations in Laughlin states.

EFFECTIVE FIELD THEORY OF SINGLE AND MULTILAYERED QUANTUM HALL FLUIDS

1994 ◽  
Vol 08 (10) ◽  
pp. 1375-1390
Author(s):  
MICHAEL R. GELLER
Keyword(s):  
Field Theory ◽  
Effective Field Theory ◽  
Quantum Hall ◽  
Complete Classification ◽  
Effective Field ◽  
Gauge Fields ◽  
Current Conservation ◽  
Two Component ◽  
Multiple Component ◽  
Chern Simons

We review an effective field theory of the quantum Hall fluid, where electron currents are expressed in terms of multiple-component gauge fields, and develop further the case of two-component fields. The form of the effective action, a simple matrix Chern-Simons action, is dictated by the principles of current conservation, dimensional analysis, gauge invariance, and by the presence of a gap. The formalism naturally describes multiple-component systems such as coupled Hall fluids in layered geometries, in addition to describing more complicated single-fluid states. We provide a complete classification of fractional quantum Hall states describable by two-component Chern-Simons gauge fields.

Sign in / Sign up

Export Citation Format

Share Document