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 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.

THEORY OF THE EDGE STATES IN FRACTIONAL QUANTUM HALL EFFECTS

1992 ◽  
Vol 06 (10) ◽  
pp. 1711-1762 ◽  
Author(s):  
XIAO-GANG WEN
Keyword(s):  
Quantum Hall ◽  
Microscopic Theory ◽  
Dynamical Theory ◽  
Effective Theory ◽  
Edge States ◽  
Filling Fraction ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Hall Effects ◽  
Laughlin States

The dynamical theory of the edge excitations of generic fractional quantum Hall (FQH) states is summarized and expanded. The low energy effective theory of the edge excitations for the most general abelian FQH states (including spin-unpolarized and multi-layer FQH states) and some non-abelian FQH states is derived using several different methods. The propagators of the electrons and the quasiparticles are calculated for the above FQH states. The microscopic theory of the edge excitations for the Laughlin states is also presented. Some simple applications of the edge theory to the transport properties of the FQH states are discussed. In particular, the tunneling between edge states is shown to be a powerful tool to probe the internal topological orders in the FQH states. It can be used to distinguish different FQH states with the same filling fraction and to detect the non-abelian FQH states in experiments.

scholarly journals Fractional quantum Hall effect in a quantum point contact at filling fraction 5/2

2007 ◽  
Vol 3 (8) ◽  
pp. 561-565 ◽  
Author(s):  
Jeffrey B. Miller ◽  
Iuliana P. Radu ◽  
Dominik M. Zumbühl ◽  
Eli M. Levenson-Falk ◽  
Marc A. Kastner ◽  
...  
Keyword(s):  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Point Contact ◽  
Fractional Quantum Hall Effect ◽  
Quantum Point Contact ◽  
Filling Fraction ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Quantum Point

scholarly journals Quantum Hall Conductivity in the Presence of Interactions

Symmetry ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 200
Author(s):  
Xi Wu ◽  
Mikhail Zubkov
Keyword(s):  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Interaction Strength ◽  
Fractional Quantum Hall Effect ◽  
Landau Levels ◽  
Hall Conductivity ◽  
Filling Fraction ◽  
Fractional Quantum ◽  
Fractional Quantum Hall

We discuss quantum Hall effect in the presence of arbitrary pair interactions between electrons. It is shown that, irrespective of the interaction strength, the Hall conductivity is given by the filling fraction of Landau levels averaged over the ground state of the system. This conclusion remains valid for both the integer and fractional quantum Hall effect.

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.

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