Conformal Field Theory of Composite Fermions

Hansson, Thor Hans; Chang, Chia Chen; Jain, J. K.; Viefers, S.

doi:10.1103/physrevlett.98.076801

Cited by 39 publications

(101 citation statements)

References 17 publications

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“…., and the construction here reduces to the one presented in Ref. 10 where it was shown that these wave functions are identical to Jain's composite fermion wave functions. The t i 's determine the densities of the n condensates that build up the state-the composite fermion state at level n is the one where all but the first of these condensates have maximal density; when t i increases the density decreases.…”

Section: Introductionmentioning

confidence: 71%

“…The state is obtained using conformal techniques generalizing the construction of the Laughlin states [3] and the Jain states [10].…”

Section: Hierarchy Wave Functionsmentioning

confidence: 99%

“…. is an expectation value in a vacuum state with an appropriately chosen background charge [3,10]. The crucial polynomial part follows directly from the operator product expansion in (3), whereas the gaussian factor is obtained from the background charge.…”

Section: Hierarchy Wave Functionsmentioning

confidence: 99%

“…10 it was shown how to construct quasihole wave functions for the Jain series, and how to relate these to Wen's general classification [6] of abelian quantum Hall fluids. An abelian fluid (on a flat manifold) at level n is specified by an n × n matrix K, an n-dimensional charge vector t, and n distinct n-dimensional vectors l (α) .…”

Section: Quasiholes and Quasielectronsmentioning

confidence: 99%

“…10, there is no local operator that will create quasielectrons. The naive guess, H −1 α , will give correlators which are not analytic in the electron coordinates, and thus not acceptable lowest Landau level wave functions.…”

Section: A Quasihole Wave Functionsmentioning

confidence: 99%

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Quantum Hall hierarchy wave functions: From conformal correlators to Tao-Thouless states

et al. 2008

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Laughlin's wave functions, describing the fractional quantum Hall effect at filling factors ν = 1/(2k + 1), can be obtained as correlation functions in conformal field theory, and recently this construction was extended to Jain's composite fermion wave functions at filling factors ν = n/(2kn+ 1). Here we generalize this latter construction and present ground state wave functions for all quantum Hall hierarchy states that are obtained by successive condensation of quasielectrons (as opposed to quasiholes) in the original hierarchy construction. By considering these wave functions on a cylinder, we show that they approach the exact ground states, the Tao-Thouless states, when the cylinder becomes thin. We also present wave functions for the multi-hole states, make the connection to Wen's general classification of abelian quantum Hall fluids, and discuss whether the fractional statistics of the quasiparticles can be analytically determined. Finally we discuss to what extent our wave functions can be described in the language of composite fermions.

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Section: Introductionmentioning

confidence: 71%

“…The state is obtained using conformal techniques generalizing the construction of the Laughlin states [3] and the Jain states [10].…”

Section: Hierarchy Wave Functionsmentioning

confidence: 99%

Section: Hierarchy Wave Functionsmentioning

confidence: 99%

Section: Quasiholes and Quasielectronsmentioning

confidence: 99%

Section: A Quasihole Wave Functionsmentioning

confidence: 99%

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Quantum Hall hierarchy wave functions: From conformal correlators to Tao-Thouless states

et al. 2008

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Quantum field theory and composite fermions in the fractional quantum Hall effect

Kossow¹

2009

Ann. Phys.

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We derive a composite fermion model for the fractional quantum Hall effect from relativistic quantum electrodynamics. With simple arguments it is shown that a special Chern Simons transformation of the Dirac electrons in four spacetime dimensions leads in the low energy limit to a single particle Hamiltonian for composite fermions in three dimensions with correction terms such as Rashba-or Dresselhaus-spin-orbit coupling and zitterbewegung. Furthermore we provide a mechanism to quantum-mechanically project the quantum fields defined in the four dimensional Minkowski space to three dimensions. This leads to a relativistic field theory and especially a composite fermion field theory in three dimension. This projection map can be combined with the projection onto a Landau level or composite fermion Landau level respectively. This results in a quasi relativistic quantum field theory on a noncommutative plane. The phenomenological models resulting from this approach are discussed and allow a systematical exploration of the effects of the spin and the condensation in a Landau level. We expect from the relativistic approach corrections in terms of spin-orbit coupling effects. From the projection onto Landau levels we expect a modification of the dispersion relation and a modified composite fermion mass. Furthermore, the BRST quantization for Chern Simons theories with compact gauge group is reviewed and the phenomenological consequences within a composite fermion model with spin are discussed. The connection to Wess Zumino Witten theories is recalled and a possible link between the corresponding central charge of the related affine Lie algebra and the composite fermion filling factor is pointed out.

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Quantum field theory and composite fermions in the fractional quantum Hall effect

Kossow

2009

Annalen der Physik

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We derive a composite fermion model for the fractional quantum Hall effect from relativistic quantum electrodynamics. With simple arguments it is shown that a special Chern Simons transformation of the Dirac electrons in four spacetime dimensions leads in the low energy limit to a single particle Hamiltonian for composite fermions in three dimensions with correction terms such as Rashba‐ or Dresselhaus‐spin‐orbit coupling and zitterbewegung. Furthermore we provide a mechanism to quantum‐mechanically project the quantum fields defined in the four dimensional Minkowski space to three dimensions. This leads to a relativistic field theory and especially a composite fermion field theory in three dimension. This projection map can be combined with the projection onto a Landau level or composite fermion Landau level respectively. This results in a quasi relativistic quantum field theory on a noncommutative plane. The phenomenological models resulting from this approach are discussed and allow a systematical exploration of the effects of the spin and the condensation in a Landau level. We expect from the relativistic approach corrections in terms of spin‐orbit coupling effects. From the projection onto Landau levels we expect a modification of the dispersion relation and a modified composite fermion mass. Furthermore, the BRST quantization for Chern Simons theories with compact gauge group is reviewed and the phenomenological consequences within a composite fermion model with spin are discussed. The connection to Wess Zumino Witten theories is recalled and a possible link between the corresponding central charge of the related affine Lie algebra and the composite fermion filling factor is pointed out.

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Conformal Field Theory of Composite Fermions

Cited by 39 publications

References 17 publications

Quantum Hall hierarchy wave functions: From conformal correlators to Tao-Thouless states

Quantum Hall hierarchy wave functions: From conformal correlators to Tao-Thouless states

Quantum field theory and composite fermions in the fractional quantum Hall effect

Quantum field theory and composite fermions in the fractional quantum Hall effect

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