scholarly journals PROPERTIES OF QUANTUM HALL SKYRMIONS FROM ANOMALIES

1998 ◽  
Vol 13 (32) ◽  
pp. 2627-2635 ◽  
Author(s):  
S. BAEZ ◽  
A. P. BALACHANDRAN ◽  
A. TRAVESSET ◽  
A. STERN
Keyword(s):  
Quantum Hall ◽  
Effective Field ◽  
Fractional Quantum Hall Effect ◽  
Spin Fluctuations ◽  
Winding Number ◽  
Anomaly Cancellation ◽  
Filling Fraction ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Chern Simons

In this letter, we introduce Fractional Quantum Hall Effect (FQHE) Skyrmions in the Chern–Simons effective field theory description, and we present a new derivation of the FQHE Skyrmions properties, namely charge and spin, which results from considerations at the edge of the Hall sample. At the boundary, we demand anomaly cancellation for the chiral edge currents, as well as, allow for the possibility of Skyrmion creation and annihilation. For the Skyrmion charge and spin, we get the values eνN Sky and νN Sky /2, respectively, where e is electron charge, ν is the filling fraction and N Sky is the Skyrmion winding number. We also add terms to the action so that the classical spin fluctuations in the bulk satisfy the standard equations of a ferromagnet and find that spin waves propagate with the classical drift velocity of the electron.

scholarly journals W∞ ALGEBRAS FROM NONCOMMUTATIVE CHERN–SIMONS THEORY

2003 ◽  
Vol 18 (18) ◽  
pp. 1215-1223 ◽  
Author(s):  
A. PINZUL ◽  
A. STERN
Keyword(s):  
Quantum Hall ◽  
Fractional Quantum Hall Effect ◽  
Simons Theory ◽  
Filling Fraction ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Algebra Of Observables ◽  
Chern Simons ◽  
Noncommutative Plane ◽  
Chern Simons Theory

We examine Chern–Simons theory written on a noncommutative plane with a "hole", and show that the algebra of observables is a nonlinear deformation of the w∞ algebra. The deformation depends on the level (the coefficient in the Chern–Simons action), and the noncommutativity parameter, which were identified, respectively, with the inverse filling fraction (minus one) and the inverse density in a recent description of the fractional quantum Hall effect. We remark on the quantization of our algebra. The results are sensitive to the choice of ordering in the Gauss law.

scholarly journals SLATER DECOMPOSITION OF LAUGHLIN STATES

1993 ◽  
Vol 07 (28) ◽  
pp. 4783-4813 ◽  
Author(s):  
GERALD V. DUNNE
Keyword(s):  
Density Operator ◽  
Quantum Hall ◽  
Fractional Quantum Hall Effect ◽  
Expectation Values ◽  
Filling Fraction ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Laughlin States ◽  
Expansion Coefficients ◽  
Slater Basis

The second-quantized form of the Laughlin states for the fractional quantum Hall effect is discussed by decomposing the Laughlin wavefunctions into the N-particle Slater basis. A general formula is given for the expansion coefficients in terms of the characters of the symmetric group, and the expansion coefficients are shown to possess numerous interesting symmetries. For expectation values of the density operator it is possible to identify individual dominant Slater states of the correct uniform bulk density and filling fraction in the physically relevant N→∞ limit.

scholarly journals A FAMILY OF NONCOMMUTATIVE GEOMETRIES

2011 ◽  
Vol 26 (29) ◽  
pp. 2213-2221 ◽  
Author(s):  
DEBABRATA SINHA ◽  
PULAK RANJAN GIRI
Keyword(s):  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Fractional Quantum Hall Effect ◽  
The Self ◽  
Filling Fraction ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Adjoint Extension ◽  
Quantum Hall System ◽  
Extension Parameter

It is shown that the noncommutativity in quantum Hall system may get modified. The self-adjoint extension of the corresponding Hamiltonian leads to a family of noncommutative geometry labeled by the self-adjoint extension parameters. We explicitly perform an exact calculation using a singular interaction and show that, when projected to a certain Landau level, the emergent noncommutative geometries of the projected coordinates belong to a one-parameter family. There is a possibility of obtaining the filling fraction of fractional quantum Hall effect by suitably choosing the value of the self-adjoint extension parameter.

scholarly journals HIERARCHICAL WAVE FUNCTIONS OF FRACTIONAL QUANTUM HALL EFFECT ON THE TORUS

1993 ◽  
Vol 07 (14) ◽  
pp. 2655-2665 ◽  
Author(s):  
DINGPING LI
Keyword(s):  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Fractional Quantum Hall Effect ◽  
Wave Functions ◽  
Simons Theory ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Chern Simons ◽  
Chern Simons Theory

One kind of hierarchical wave functions of Fractional Quantum Hall Effect on the torus is constructed. We find that the wave functions are closely related to the wave functions of generalized Abelian Chern-Simons theory.

THE CHERN–SIMONS–LANDAU–GINZBURG THEORY OF THE FRACTIONAL QUANTUM HALL EFFECT

1992 ◽  
Vol 06 (01) ◽  
pp. 25-58 ◽  
Author(s):  
SHOU CHENG ZHANG
Keyword(s):  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Mean Field ◽  
Fractional Quantum Hall Effect ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Physical Consequences ◽  
Systematic Derivation ◽  
Chern Simons

This paper gives a systematic review of a field theoretical approach to the fractional quantum Hall effect (FQHE) that has been developed in the past few years. We first illustrate some simple physical ideas to motivate such an approach and then present a systematic derivation of the Chern–Simons–Landau–Ginzburg (CSLG) action for the FQHE, starting from the microscopic Hamiltonian. It is demonstrated that all the phenomenological aspects of the FQHE can be derived from the mean field solution and the small fluctuations of the CSLG action. Although this formalism is logically independent of Laughlin's wave function approach, their physical consequences are equivalent. The CSLG theory demonstrates a deep connection between the phenomena of superfluidity and the FQHE, and can provide a simple and direct formalism to address many new macroscopic phenomena of the FQHE.

NON-RENORMALIZATION THEOREM IN CHERN-SIMONS THEORIES AND FRACTIONAL QUANTUM HALL EFFECT

1992 ◽  
Vol 07 (07) ◽  
pp. 611-617 ◽  
Author(s):  
A.A. OVCHINNIKOV
Keyword(s):  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Statistical Parameter ◽  
Fractional Quantum Hall Effect ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Chern Simons ◽  
Exact Cancellation

We prove the non-renormalization theorem resulting in the exact cancellation of Chern-Simons term (and superconductivity) in systems of both free and interacting anyons with the statistical parameter 1/N. The theorem is used to prove the quantization of transverse conductance in the proposed second-quantized fermionic description of fractional quantum Hall effect.

Sign in / Sign up

Export Citation Format

Share Document