Thirty Years of Composite Fermions and Beyond

Jain, J. K.

doi:10.1142/9789811217494_0001

Cited by 5 publications

(7 citation statements)

References 231 publications

(396 reference statements)

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“…• The parameter matching (3.31) for fractional fillings involves rescaling the density ρ 0 (λ) and the magnetic length 2 → √ m 2 . This is different from the naive scaling 2 → m 2 suggested by the composite fermion map [8]. A simple, intuitive argument for this result is presently missing.…”

Section: Jhep05(2021)120contrasting

confidence: 61%

“…The study of low-energy bulk physics above the topological limit is somehow less developed. The Jain theory of flux attachment and composite fermion excitations has been confirmed experimentally and numerically [8], and it remarkably extends to relativistic regimes for filling fractions near one half [9]. Flux attachment has been successfully described by mean field theory [10,11] and Hartree-Fock approximations [12].…”

Section: Jhep05(2021)120mentioning

confidence: 78%

“…• It can be shown that the modified derivatives in (2.22) are actually arising by coupling electrons to a Chern-Simons statistical field with coupling constant 1/2s, that "attaches and even number of flux quanta to electrons" [11]. Therefore the similarity transformation (2.22) is actually the Jain composite-fermion map between integer and Laughlin Hall states [8].…”

Section: Jhep05(2021)120mentioning

confidence: 99%

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W-infinity symmetry in the quantum hall effect beyond the edge

Cappelli

Maffi

2021

J. High Energ. Phys.

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The description of chiral quantum incompressible fluids by the W∞ symmetry can be extended from the edge, where it encompasses the conformal field theory approach, to the non-conformal bulk. The two regimes are characterized by excitations with different sizes, energies and momenta within the disk geometry. In particular, the bulk quantities have a finite limit for large droplets. We obtain analytic results for the radial shape of excitations, the edge reconstruction phenomenon and the energy spectrum of density fluctuations in Laughlin states.

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Section: Jhep05(2021)120contrasting

confidence: 61%

Section: Jhep05(2021)120mentioning

confidence: 78%

Section: Jhep05(2021)120mentioning

confidence: 99%

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W-infinity symmetry in the quantum hall effect beyond the edge

Cappelli

Maffi

2021

J. High Energ. Phys.

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“…In the GaAs/AlGaAs 2D electron system, a double degeneracy of Landau levels due to electronspin, is removed by a small Zeeman spin splitting, gµ B B , comparable to the correlation energy. Then, a change of the Zeeman splitting relative to the correlation energy can lead to a re-ordering between spin polarized, partially polarized, and unpolarized many body ground states at a constant filling factor [19][20][21][22][23][24] . Halperin identified the possibility of a spin-unpolarized FQHE ground state having a lower energy than the spin polarized ground state at, e.g., ν = 2/5 , for a system exhibiting a small spin splitting 19 .…”

mentioning

confidence: 99%

Size dependence- and induced transformations- of fractional quantum Hall effects under tilted magnetic fields

Wijewardena

Nanayakkara

Kriisa

et al. 2022

Sci Rep

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Two-dimensional electron systems subjected to high transverse magnetic fields can exhibit Fractional Quantum Hall Effects (FQHE). In the GaAs/AlGaAs 2D electron system, a double degeneracy of Landau levels due to electron-spin, is removed by a small Zeeman spin splitting, $$g \mu _B B$$ g μ B B , comparable to the correlation energy. Then, a change of the Zeeman splitting relative to the correlation energy can lead to a re-ordering between spin polarized, partially polarized, and unpolarized many body ground states at a constant filling factor. We show here that tuning the spin energy can produce fractionally quantized Hall effect transitions that include both a change in $$\nu$$ ν for the $$R_{xx}$$ R xx minimum, e.g., from $$\nu = 11/7$$ ν = 11 / 7 to $$\nu = 8/5$$ ν = 8 / 5 , and a corresponding change in the $$R_{xy}$$ R xy , e.g., from $$R_{xy}/R_{K} = (11/7)^{-1}$$ R xy / R K = ( 11 / 7 ) - 1 to $$R_{xy}/R_{K} = (8/5)^{-1}$$ R xy / R K = ( 8 / 5 ) - 1 , with increasing tilt angle. Further, we exhibit a striking size dependence in the tilt angle interval for the vanishing of the $$\nu = 4/3$$ ν = 4 / 3 and $$\nu = 7/5$$ ν = 7 / 5 resistance minima, including “avoided crossing” type lineshape characteristics, and observable shifts of $$R_{xy}$$ R xy at the $$R_{xx}$$ R xx minima- the latter occurring for $$\nu = 4/3, 7/5$$ ν = 4 / 3 , 7 / 5 and the 10/7. The results demonstrate both size dependence and the possibility, not just of competition between different spin polarized states at the same $$\nu$$ ν and $$R_{xy}$$ R xy , but also the tilt- or Zeeman-energy-dependent- crossover between distinct FQHE associated with different Hall resistances.

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“…3.5. Furthermore, the CF theory can also map an electronic FQH state to a CF FQH state [71][72][73][74][75][76].…”

Section: Brief Review On the Composite Fermion Theorymentioning

confidence: 99%

Graviton modes in fractional quantum hall liquids

Wang¹

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The fractional quantum Hall fluid is a two-dimensional quantum fluid of electrons subject to a strong magnetic field at low temperatures. Neutral excitations in a fractional quantum Hall droplet define the incompressibility gap of the topological phase. Among these states, there are some specific modes in the long-wavelength limit that can be understood as "spin-2 gravitons". In this thesis, we will introduce a set of analytical results for the energy gap of the graviton modes for model Hamiltonians in the thermodynamic limit, which is governed by a well-defined and universal characteristic tensor. These results can help to construct model Hamiltonians for the graviton modes of different FQH phases and elucidate a hierarchical structure of conformal Hilbert spaces (null spaces of model Hamiltonians) containing the graviton modes and their corresponding ground states. An isomorphism can be defined for these conformal Hilbert spaces, and the mapping between them can be regarded as a more rigorous and general reinterpretation of the composite fermionization of FQH states, with naturally emergent composite fermions (each consisting of one electron and an even number of fluxes). The results from exact diagonalization will be shown, which confirm that for gapped phases, low-lying neutral excitations can undergo a phase transition even when the ground state remains in the same phase. Furthermore, the gaplessness of the Gaffnian state could be testified based on this formalism with further numerical experiments. Recently there has been numerical evidence implying the signature of multiple graviton modes. We will introduce the microscopic theory for the emergence of multiple gravitons in fractional quantum Hall droplets based on composite fermionization and the well-defined particle-hole conjugate within a specific conformal Hilbert space. This reveals the dynamical nature of this phenomenon and provides theoretical insights into the chirality and the "merging and splitting" behaviors of the graviton modes. The experimental relevance of multiple graviton modes will be discussed. The microscopic theory of gravitons can also provide valuable insights into the field-theoretical approaches.

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Thirty Years of Composite Fermions and Beyond

Cited by 5 publications

References 231 publications

W-infinity symmetry in the quantum hall effect beyond the edge

W-infinity symmetry in the quantum hall effect beyond the edge

Size dependence- and induced transformations- of fractional quantum Hall effects under tilted magnetic fields

Graviton modes in fractional quantum hall liquids

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