scholarly journals SOLITONS ON NONCOMMUTATIVE TORUS AS ELLIPTIC CALOGERO–GAUDIN MODELS, BRANES AND LAUGHLIN WAVE FUNCTIONS

2003 ◽  
Vol 18 (14) ◽  
pp. 2477-2500 ◽  
Author(s):  
BO-YU HOU ◽  
DAN-TAO PENG ◽  
KANG-JIE SHI ◽  
RUI-HONG YUE
Keyword(s):  
Quantum Hall ◽  
Moment Map ◽  
Simons Theory ◽  
Noncommutative Torus ◽  
The Moment ◽  
Gaudin Models ◽  
Laughlin Wave Function ◽  
Marked Points ◽  
Chern Simons ◽  
Chern Simons Theory

For the noncommutative torus [Formula: see text], in the case of the noncommutative parameter [Formula: see text], we construct the basis of Hilbert space ℋn in terms of θ functions of the positions zi of n solitons. The wrapping around the torus generates the algebra [Formula: see text], which is the Zn × Zn Heisenberg group on θ functions. We find the generators g of a local elliptic su (n), which transform covariantly by the global gauge transformation of [Formula: see text]. By acting on ℋn we establish the isomorphism of [Formula: see text] and g. We embed this g into the L-matrix of the elliptic Gaudin and Calogero–Moser models to give the dynamics. The moment map of this twisted cotangent [Formula: see text] bundle is matched to the D-equation with the Fayet–Illiopoulos source term, so the dynamics of the noncommutative solitons become that of the brane. The geometric configuration (k, u) of the spectral curve det |L(u) - k| = 0 describes the brane configuration, with the dynamical variables zi of the noncommutative solitons as the moduli T⊗ n/Sn. Furthermore, in the noncommutative Chern–Simons theory for the quantum Hall effect, the constrain equation with quasiparticle source is identified also with the moment map equation of the noncommutative [Formula: see text] cotangent bundle with marked points. The eigenfunction of the Gaudin differential L-operators as the Laughlin wave function is solved by Bethe ansatz.

scholarly journals Dualities in Quantum Hall System and Noncommutative Chern-Simons Theory

2002 ◽  
Vol 2002 (01) ◽  
pp. 002-002 ◽  
Author(s):  
Alexander Gorsky ◽  
Ian I Kogan ◽  
Chris Korthals-Altes
Keyword(s):  
Quantum Hall ◽  
Simons Theory ◽  
Quantum Hall System ◽  
Chern Simons ◽  
Chern Simons Theory

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.

scholarly journals QUANTUM HALL STRIPES: CHERN–SIMONS THEORY AND ORIENTATIONAL MECHANISMS

2001 ◽  
Vol 15 (13) ◽  
pp. 1905-1914 ◽  
Author(s):  
BERND ROSENOW ◽  
STEFAN SCHEIDL
Keyword(s):  
Charge Density Wave ◽  
Electron Gas ◽  
Density Wave ◽  
Quantum Hall ◽  
Simons Theory ◽  
Dimensional Electron ◽  
Half Filling ◽  
Dimensional Electron Gas ◽  
Chern Simons ◽  
Chern Simons Theory

We develop a bosonic Chern–Simons theory to describe a two-dimensional electron gas in intermediate magnetic fields. Within this approach, inhomogeneous states emerge in analogy to the intermediate state of a superconductor. At half filling of the highest Landau level we find unidirectional charge-density-wave (CDW) solutions. With a semiclassical calculation we give an intuitive explanation of the change of CDW orientation in the presence of an in-plane magnetic field. An anisotropy in the electron band mass is suggested as a possible source of the reproducible orientation of the CDW.

scholarly journals CHERN–SIMONS THEORY OF FRACTIONAL QUANTUM HALL EFFECT IN (PSEUDO) MASSLESS DIRAC ELECTRONS

2011 ◽  
Vol 25 (20) ◽  
pp. 2779-2785
Author(s):  
HUABI ZENG
Keyword(s):  
Quantum Hall ◽  
Effective Field ◽  
Simons Theory ◽  
Arbitrary Integer ◽  
Fractional Quantum ◽  
Hall Conductance ◽  
Fractional Quantum Hall ◽  
Topological Excitations ◽  
Chern Simons ◽  
Chern Simons Theory

We derive the effective-field theory from the microscopic Hamiltonian of interacting two-dimensional (pseudo) Dirac electrons by performing a statistic gauge transformation. The quantized Hall conductance are expected to be σxy=e2/h(2k-1) where k is arbitrary integer. There are also topological excitations which have fractional charge and obey fractional statistics.

scholarly journals SINGLE-MODE APPROXIMATION AND EFFECTIVE CHERN–SIMONS THEORIES FOR QUANTUM HALL SYSTEMS

2003 ◽  
Vol 17 (31n32) ◽  
pp. 5875-5891 ◽  
Author(s):  
K. SHIZUYA
Keyword(s):  
Landau Level ◽  
Quantum Hall ◽  
Single Mode ◽  
Collective Excitations ◽  
Effective Theory ◽  
Simons Theory ◽  
Quantum Hall Systems ◽  
Single Mode Approximation ◽  
Chern Simons ◽  
Chern Simons Theory

A unified description of elementary and collective excitations in quantum Hall systems is presented within the single-mode approximation (SMA) framework, with emphasis on revealing an intimate link with Chern–Simons theories. It is shown that for a wide class of quantum Hall systems the SMA in general yields, as an effective theory, a variant of the bosonic Chern–Simons theory. For single-layer systems the effective theory agrees with the standard Chern–Simons theory at long wavelengths whereas substantial deviations arise for collective excitations in bilayer systems. It is suggested, in particular, that Hall-drag experiments would be a good place to detect out-of-phase collective excitations inherent to bilayer systems. It is also shown that the intra-Landau-level modes bear a similarity in structure (though not in scale) to the inter-Landau-level modes, and its implications on the composite-fermion and composite-boson theories are discussed.

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