Classification of Abelian quantum Hall states and matrix formulation of topological fluids

Wen, Xiao-Gang; Zee, A.

doi:10.1103/physrevb.46.2290

Cited by 469 publications

(660 citation statements)

References 38 publications

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“…Thus p = 1 corresponds to the Laughlin series. In particular, also for p = 1, this is the form of the action that follows from hydrodynamic arguments [6,11,12,13,14]. It is straightforward to show [8] that this theory leads to the correct value of the Hall conductivity…”

Section: The Non-commutative Effective Action For the Statisticalmentioning

confidence: 99%

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Non-commutative Chern–Simons for the quantum Hall system and duality

2002

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The quantum Hall system is known to have two mutually dual Chern-Simons descriptions, one associated with the hydrodynamics of the electron fluid, and another associated with the statistics. Recently, Susskind has made the claim that the hydrodynamic Chern-Simons theory should be considered to have a non-commutative gauge symmetry. The statistical Chern-Simons theory has a perturbative momentum expansion. In this paper, we study this perturbation theory and show that the effective action, although commutative at leading order, is non-commutative. This conclusion is arrived at through a careful study of the three-point function of ChernSimons gauge fields. The non-commutative gauge symmetry of this system is thus a quantum symmetry, which we show can only be fully realized only through the inclusion of all orders in perturbation theory. We discuss the duality between the two non-commutative descriptions.

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Section: The Non-commutative Effective Action For the Statisticalmentioning

confidence: 99%

“…[7,8,27], and it corresponds to 2n fluxes being attached to each fermion. Conversely, the gauge field b µ is the hydrodynamic field used by Wen [5,11,12]. As noted in Ref.…”

Section: Duality Invariant Formalism: Commutative Limitmentioning

confidence: 99%

Non-commutative Chern–Simons for the quantum Hall system and duality

2002

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“…This setup has been used by several authors, in particular by X. G. Wen (1989), J. Frohlich, T. Kerler (1991) and X. G. Wen, A. Zee (1992). We shall, however, only scratch on this threory and show | using an argument b y J .…”

Section: The Laughlin Argumentmentioning

confidence: 99%

Geometric Properties of Transport in Quantum Hall Systems

Richter¹,

Seiler²

2000

Geometry and Quantum Physics

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“…An RCFT can be defined now imposing on u(1) ⊗m the following compactification condition fixed by K m,p [43,38]:…”

Section: (328)mentioning

confidence: 99%

“…In section 3, we derive the main identities among the η-function of Dedekind, the characters of the W m chiral algebra and the characters of the affine level 1 su(m) 1 , evaluated at the so called principal element of type ρ of B. Kostant [36]. In section 4, we recall the definition of the Γ θ -RCFT m-component free bosons u(1) Km,p [23,43,15,10]. The corresponding chiral algebra A( u(1) Km,p ) is identified together with the finite set of h.w.…”

Section: Introductionmentioning

confidence: 99%

A new rational conformal field theory extension of the fully degenerate W_1+∞^(m)

Cristofano

Marotta

Niccoli

2006

J. High Energy Phys.

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A new Rational Conformal Field Theory extension of the fully degenerate W (m) 1+∞Gerardo Cristofano 1 , Vincenzo Marotta 1 , Giuliano Niccoli 2 AbstractWe found new identities among the Dedekind η-function, the characters of the W m algebra and those of the level 1 affine Lie algebra su(m) 1 . They allow to characterize the Z m -orbifold of the m-component free bosons u(1) Km,p (our theory TM) as an extension of the fully degenerate representations of W (m) 1+∞ . In particular, TM is proven to be a Γ θ -RCFT extension of the chiral fully degenerate W (m) 1+∞ .

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Classification of Abelian quantum Hall states and matrix formulation of topological fluids

Cited by 469 publications

References 38 publications

Non-commutative Chern–Simons for the quantum Hall system and duality

Non-commutative Chern–Simons for the quantum Hall system and duality

Geometric Properties of Transport in Quantum Hall Systems

A new rational conformal field theory extension of the fully degenerate W_1+∞^(m)

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Classification of Abelian quantum Hall states and matrix formulation of topological fluids

Cited by 469 publications

References 38 publications

Non-commutative Chern–Simons for the quantum Hall system and duality

Non-commutative Chern–Simons for the quantum Hall system and duality

Geometric Properties of Transport in Quantum Hall Systems

A new rational conformal field theory extension of the fully degenerate W1+∞(m)

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Product

Resources

About

A new rational conformal field theory extension of the fully degenerate W_1+∞^(m)