Hopf Term for a Two-Dimensional Electron Gas

Volovik, G. E.; Yakovenko, Victor M.

doi:10.1103/physrevlett.79.3791

Cited by 46 publications

(20 citation statements)

References 9 publications

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“…It has been claimed 8 that they are fermionic due to an induced Hopf term. However, objections have been raised 9 against the derivation presented therein. An induced Hopf term with the appropriate coefficient has also been obtained, but within an ansatz, in Ref.…”

Section: Introductionmentioning

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: Introductionmentioning

confidence: 99%

Quantum Hall ferromagnets: Induced topological term and electromagnetic interactions

Ray

1999

Phys. Rev. B

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“…Using (2) in (1) one realizes that: (i) The second term in the curly brackets-the total time derivativevanishes and (ii) the first term in the curly brackets yields…”

mentioning

confidence: 99%

Apel and Bychkov Reply:

Apel

Bychkov

1997

Phys. Rev. Lett.

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“…We also find 6) which shows that, in each sector, configurations are characterized by another integer, called the Hopf (or instanton) number. To express the Hopf number as a term in the action, conventionally one considers [7] …”

Section: Introductionmentioning

confidence: 79%

“…Explicitly, if we use, e.g., the Euler angle decomposition for the element g 21 , 6) then the unitary operator implementing the left-action is given by…”

Section: Soliton Operatorsmentioning

confidence: 99%

Hopf term, fractional spin and soliton operators in the O(3) non-linear sigma model

Kimura¹,

Kobayashi²,

Tsutsui³

1998

Nuclear Physics B

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Abstract. We re-examine three issues, the Hopf term, fractional spin and the soliton operators, in the 2 + 1 dimensional O(3) nonlinear sigma model based on the adjoint orbit parametrization (AOP) introduced earlier. It is shown that the Hopf term is well-defined for configurations of any soliton charge Q if we adopt a time independent boundary condition at spatial infinity. We then develop the Hamiltonian formulation of the model in the AOP and thereby argue that the well-known Q 2 -formula for fractional spin holds only for a restricted class of configurations. Operators which create states of given classical configurations of any soliton number in the (physical) Hilbert space are constructed. Our results clarify some of the points which are crucial for the above three topological issues and yet have remained obscure in the literature.

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Hopf Term for a Two-Dimensional Electron Gas

Cited by 46 publications

References 9 publications

Quantum Hall ferromagnets: Induced topological term and electromagnetic interactions

Quantum Hall ferromagnets: Induced topological term and electromagnetic interactions

Apel and Bychkov Reply:

Hopf term, fractional spin and soliton operators in the O(3) non-linear sigma model

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