Quantum Hall effect in higher dimensions

Karabali, Dimitra; Nair, V. P.

doi:10.1016/s0550-3213(02)00634-x

Cited by 185 publications

(316 citation statements)

References 10 publications

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“…Since then further generalizations and analyses in higher dimensions and different geometries have been carried out by many authors [13]- [20]. The general framework is the following.…”

Section: Quantum Hall Effect In Higher Dimensionsmentioning

confidence: 99%

Quantum Hall effect in higher dimensions, matrix models and fuzzy geometry

Karabali¹,

Nair²

2006

J. Phys. A: Math. Gen.

105

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We give a brief review of quantum Hall effect in higher dimensions and its relation to fuzzy spaces. For a quantum Hall system, the lowest Landau level dynamics is given by a onedimensional matrix action whose large N limit produces an effective action describing the gauge interactions of a higher dimensional quantum Hall droplet. The bulk action is a Chern-Simons type term whose anomaly is exactly cancelled by the boundary action given in terms of a chiral, gauged Wess-Zumino-Witten theory suitably generalized to higher dimensions. We argue that the gauge fields in the Chern-Simons action can be understood as parametrizing the different ways in which the large N limit of the matrix theory is taken.The possible relevance of these ideas to fuzzy gravity is explained. Other applications are also briefly discussed.

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“…Since then further generalizations and analyses in higher dimensions and different geometries have been carried out by many authors [13]- [20]. The general framework is the following.…”

Section: Quantum Hall Effect In Higher Dimensionsmentioning

confidence: 99%

Quantum Hall effect in higher dimensions, matrix models and fuzzy geometry

Karabali¹,

Nair²

2006

J. Phys. A: Math. Gen.

105

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“…Notice that the U (1) part of the gauge field does not contribute in (45). 2 Similarly the action of two right operators R α on a symbol produces the following expression…”

Section: Qhe On Cp Kmentioning

confidence: 99%

“…The higher dimensional generalization exhibits features similar to the twodimensional case, such as incompressibility and gapless edge excitations, among other things. In a series of papers [2]- [6] we generalized the original Zhang-Hu construction of QHE on S 4 to arbitrary even dimensions by formulating the quantum Hall effect on the complex projective spaces CP k .…”

Section: Introductionmentioning

confidence: 99%

Bosonization of the lowest Landau level in arbitrary dimensions: Edge and bulk dynamics

Karabali¹

2006

Nuclear Physics B

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We discuss the bosonization of nonrelativistic fermions interacting with non-Abelian gauge fields in the lowest Landau level in the framework of higher dimensional quantum Hall effect. The bosonic action is a one-dimensional matrix action, which can also be written as a noncommutative field theory, invariant under W N transformations. The requirement that the usual gauge transformation should be realized as a W N transformation provides an analog of a Seiberg-Witten map, which allows us to express the action purely in terms of bosonic fields. The semiclassical limit of this, describing the gauge interactions of a higher dimensional, non-Abelian quantum Hall droplet, produces a bulk Chern-Simons type term whose anomaly is exactly cancelled by a boundary term given in terms of a gauged Wess-Zumino-Witten action.

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“…23 on the compact S 4 sphere by coupling large spin fermions to the SU(2) magnetic monopole, in which fermion spin scales with the radius as R 2 . Later on various generalizations to other manifold have been developed [24][25][26][27][28] . Two of the authors have generalized the LLs of non-relativistic fermions to arbitrary dimensional flat space R D 29 .…”

mentioning

confidence: 99%

Two- and three-dimensional topological insulators with isotropic and parity-breaking Landau levels

Zhou

2012

Phys. Rev. B

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We investigate topological insulating states in both two and three dimensions with the harmonic potential and strong spin-orbit couplings breaking the inversion symmetry. Landau-level like quantization appear with the full 2D and 3D rotational symmetry and time-reversal symmetry. Inside each band, states are labeled by their angular momenta over which energy dispersions are strongly suppressed by spin-orbit coupling to nearly flat. The radial quantization generates energy gaps between neighboring bands at the order of the harmonic frequency. Helical edge or surface states appear on open boundaries characterized by the Z2 index. These Hamiltonians can be viewed from the dimensional reduction of the high dimensional quantum Hall states in 3D and 4D flat spaces. These states can be realized with ultra-cold fermions inside harmonic traps with the synthetic gauge fields.

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Quantum Hall effect in higher dimensions

Cited by 185 publications

References 10 publications

Quantum Hall effect in higher dimensions, matrix models and fuzzy geometry

Quantum Hall effect in higher dimensions, matrix models and fuzzy geometry

Bosonization of the lowest Landau level in arbitrary dimensions: Edge and bulk dynamics

Two- and three-dimensional topological insulators with isotropic and parity-breaking Landau levels

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