A matrix model for bilayered quantum Hall systems

Jellal, Ahmed; Schreiber, Michael

doi:10.1088/0305-4470/37/9/007

Cited by 5 publications

(12 citation statements)

References 30 publications

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“…This exactly coincides with that constructed by Goerbig and Regnault [17] and what we have proposed [28] in terms of the matrix model and non-commutative Chern-Simom theories. Using the mapping (103), it is easy to show that (95) takes the form…”

supporting

confidence: 92%

“…This allowed them to discuss different issues and predict some filling factors. This wavefunction is related to that we have proposed [28], in general way, by using the matrix model and non-commutative Chern-Simons theories. In section 4, we give different discussions about the matter.…”

Section: Anomalous Fqhe On Planesupporting

confidence: 53%

“…This is seen as a direct extension of the Halperin wavefunction [16]. We note that the proposed state is related to our ground state configuration [28] realized in terms of the matrix model and non-commutative Chern-Simons theories. To consider the higher Landau levels on S 2 , we build a SU (N ) wavefunction generalizing those of Haldane [23] and corresponding to different filling factors [29] …”

Section: Introductionmentioning

confidence: 54%

“…This has been done by using our early work [28] related to the matrix model and non-commutative Chern-Simons theories. Our states allowed us to generalize their partners on the planar limit [17] and describe different filling factors.…”

Section: Discussionmentioning

confidence: 99%

“…Among them, we cite that constructed by Goerbig and Regnault [17] to solve some problems brought by other theories like for instance that developed in [11]. However, this wavefunction is sharing many common features with our early proposal [28]. On the other hand, the Goerbig and Regnault states are a direct extended version of those of the Laughlin [22] as well as Halperin [16].…”

Section: Su (N ) Wavefunctionmentioning

confidence: 96%

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Anomalous quantum Hall effect on sphere

Jellal

2008

Nuclear Physics B

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We study the anomalous quantum Hall effect exhibited by the relativistic particles living on two-sphere S 2 and submitted to a magnetic monopole. We start by establishing a direct connection between the Dirac and Landau operators through the Pauli-Schrödinger Hamiltonian H SP s . This will be helpful in the sense that the Dirac eigenvalues and eigenfunctions will be easily derived. In analyzing H SP s spectrum, we show that there is a composite fermion nature supported by the presence of two effective magnetic fields. For the lowest Landau level, we argue that the basic physics of graphene is similar to that of two-dimensional electron gas, which is in agreement with the planar limit. For the higher Landau levels, we propose a SU (N ) wavefunction for different filling factors that captures all symmetries. Focusing on the graphene case, i.e. N = 4, we give different configurations those allowed to recover some known results.

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supporting

confidence: 92%

Section: Anomalous Fqhe On Planesupporting

confidence: 53%

Section: Introductionmentioning

confidence: 54%

Section: Discussionmentioning

confidence: 99%

Section: Su (N ) Wavefunctionmentioning

confidence: 96%

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Anomalous quantum Hall effect on sphere

Jellal

2008

Nuclear Physics B

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Supersymmetric Embedding of the Quantum Hall Matrix Model

Gates

Jellal

Saidi³

et al. 2004

J. High Energy Phys.

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We develop a supersymmetric extension of the Susskind-Polychronakos matrix theory for the quantum Hall fluids. This is done by considering a system combining two sets of different particles and using both a component field method as well as world line superfields. Our construction yields a class of models for fractional quantum Hall systems with two phases U and D involving, respectively N 1 bosons and N 2 fermions. We build the corresponding supersymmetric matrix action, derive and solve the supersymmetric generalization of the Susskind-Polychronakos constraint equations. We show that the general U (N ) gauge invariant solution for the ground state involves two configurations parameterized by the bosonic contribution k 1 (integer) and in addition a new degree of freedom k 2 , which is restricted to 0 and 1. We study in detail the two particular values of k 2 and show that the classical (Susskind) filling factor ν receives no quantum correction. We conclude that the Polychronakos effect is exactly compensated by the opposite fermionic contributions.

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Jain states in a matrix theory of the quantum Hall effect

Cappelli¹,

Rodriguez²

2006

J. High Energy Phys.

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The U(N) Maxwell-Chern-Simons matrix gauge theory is proposed as an extension of Susskind's noncommutative approach. The theory describes D0-branes, nonrelativistic particles with matrix coordinates and gauge symmetry, that realize a matrix generalization of the quantum Hall effect. Matrix ground states obtained by suitable projections of higher Landau levels are found to be in one-to-one correspondence with the expected Laughlin and Jain hierarchical states. The Jain composite-fermion construction follows by gauge invariance via the Gauss law constraint. In the limit of commuting, "normal" matrices the theory reduces to eigenvalue coordinates that describe realistic electrons with Calogero interaction. The Maxwell-Chern-Simons matrix theory improves earlier noncommutative approaches and could provide another effective theory of the fractional Hall effect.. This is actually the Laughlin wave function at filling ν = 1/(k + 1) [5], upon interpreting the eigenvalues as the coordinates of N planar electrons in the lowest Landau level. Therefore, the celebrated Laughlin state was shown to be the exact ground state of the matrix theory that is completely determined by gauge invariance. This is the nicest result obtained in the matrix (noncommutative) approach.In spite of these findings, the Chern-Simons matrix model so far presented some difficulties that limited its applicability as a theory of the fractional Hall effect [20]:• The Chern-Simons matrix model does not possess quasi-particle excitations, only quasi-holes can be realized [14].• The Jain states with the filling fractions, ν = m/(mk + 1), m = 2, 3, . . ., cannot be realized in the theory, even including more boundary terms [15].• Even if the Laughlin wave function is obtained, the measure of integration differs from that of electrons in the lowest Landau level, owing to the noncommutativity of matrices [18]. As shown in Ref.[1], the ground state properties of the matrix theory and of the Laughlin state agree at long distances but differ microscopically.• Owing to the inherent noncommutativity, it is also difficult to match matrix observables with electron quantities of the quantum Hall effect [19].In this paper, we show that some of these problems can be overcome by upgrading the Chern-Simons model to the Maxwell-Chern-Simons matrix theory. This includes an additional kinetic term quadratic in time derivatives and the potential V = −gTr [X 1 , X 2 ] 2 , parametrized by the positive coupling constant g. All the terms in the action are fixed by the gauge principle because they are obtained by dimensional reduction of the threedimensional Maxwell-Chern-Simons theory. The matrix theory has been discussed in the literature of string theory as the low-energy effective theory of a stack of N D0-branes on certain higher-brane configurations [24]; in particular, D0-branes have been proposed as fundamental degrees of freedom in string theory [3].In section two, we introduce the Maxwell-Chern-Simons matrix theory, quantize the Hamiltonian and discuss the Gauss-law con...

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A matrix model for bilayered quantum Hall systems

Cited by 5 publications

References 30 publications

Anomalous quantum Hall effect on sphere

Anomalous quantum Hall effect on sphere

Supersymmetric Embedding of the Quantum Hall Matrix Model

Jain states in a matrix theory of the quantum Hall effect

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