The Electromagnetic Interactions of Electrons in the Lowest Landau Level

Ray, Rashmi; Sakita, B.

doi:10.1006/aphy.1994.1020

Cited by 18 publications

(26 citation statements)

References 10 publications

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“…The purely electromagnetic terms are familiar from previous studies concerning the electromagnetic effective action of spinless quantum Hall fermions. 16,17 From the effective action, we can readily compute the mean electromagnetic currents in the spin-textured ͑excited͒ state.…”

Section: ͑324͒mentioning

confidence: 99%

Quantum Hall ferromagnets: Induced topological term and electromagnetic interactions

Ray

1999

Phys. Rev. B

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The ϭ1 quantum Hall ground state in materials such as GaAs is well known to be ferromagnetic in nature. The exchange part of the Coulomb interaction provides the necessary attractive force to align the electronic spins spontaneously. The gapless Goldstone modes are the angular deviations of the magnetization vector from its fixed ground-state orientation. Furthermore, the system is known to support electrically charged spin skyrmion configurations. It has been claimed in the literature that these skyrmions are fermionic owing to an induced topological Hopf term in the effective action governing the Goldstone modes. However, objections have been raised against the method by which this term has been obtained from the microscopics of the system. In this paper, we use the technique of the derivative expansion to derive, in an unambiguous manner, the effective action of the angular degrees of freedom, including the Hopf term. Furthermore, we have coupled perturbative electromagnetic fields to the microscopic fermionic system in order to study their effect on the spin excitations. We have obtained an elegant expression for the electromagnetic coupling of the angular variables describing these spin excitations. ͓S0163-1829͑99͒02240-7͔

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Section: ͑324͒mentioning

confidence: 99%

Quantum Hall ferromagnets: Induced topological term and electromagnetic interactions

Ray

1999

Phys. Rev. B

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“…The second term is the edge contribution. From (4.5) and (8.4), we see that This is just a chiral current moving with a velocity v = E B in agreement with [7], [8].…”

Section: Edge Current In a Quantum Hall Dropletmentioning

confidence: 69%

“…The effective action for planar electrons in a strong magnetic field coupled minimally to perturbative slowly-varying electromagnetic fields has already been given in [6], [7]. Here, we discuss the structure of the current operators arising from this effective action as a natural extension to what has been discussed in the earlier sections.…”

Section: Minimal Coupling To Electromagnetismmentioning

confidence: 85%

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Effective Interactions of Planar Fermions in a Strong Magnetic Field — The Effect of Landau Level Mixing

Ray

Gat

1994

Mod. Phys. Lett. B

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We obtain expressions for the current operator in the lowest Landau level (L.L.L.) field theory, where higher Landau level mixing due to various external and interparticle interactions is sytematically taken into account. We consider the current operators in the presence of electromagnetic interactions, both Coulomb and time-dependent, as well as local four-fermi interactions. The importance of Landau level mixing for long-range interactions is especially emphasized. We also calculate the edge-current for a finite sample.

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“…Thus we have two von Neumann algebras, which become infinite dimensional as we take n → ∞. The state corresponding to (22), expressed in terms of the algebra as a density matrix, can be written, upon using (29), as…”

Section: The Spectrum Of the Modular Operator For The ν = 1 Hallmentioning

confidence: 99%

Entanglement for quantum Hall states and a generalized Chern-Simons form

Nair

2020

Phys. Rev. D

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We analyze some features of the entanglement entropy for an integer quantum Hall state (ν ¼ 1) in comparison with ideas from relativistic field theory and noncommutative geometry. The spectrum of the modular operator, for a restricted class of states, is shown to be similar to the case of field theory or a type III 1 von Neumann algebra. We present arguments that the main part of the dependence of the entanglement entropy on background fields and geometric data such as the spin connection is given by a generalized Chern-Simons form. Implications of this result for bringing together ideas of noncommutative geometry, entropy and gravity are briefly commented upon.

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The Electromagnetic Interactions of Electrons in the Lowest Landau Level

Cited by 18 publications

References 10 publications

Quantum Hall ferromagnets: Induced topological term and electromagnetic interactions

Quantum Hall ferromagnets: Induced topological term and electromagnetic interactions

Effective Interactions of Planar Fermions in a Strong Magnetic Field — The Effect of Landau Level Mixing

Entanglement for quantum Hall states and a generalized Chern-Simons form

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