The enigma of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>ν</mml:mi><mml:mo>=</mml:mo><mml:mn>2</mml:mn><mml:mo>+</mml:mo><mml:mn>3</mml:mn><mml:mo>/</mml:mo><mml:mn>8</mml:mn></mml:mrow></mml:math>fractional quantum Hall effect

Hutasoit, Jimmy A.; Balram, Ajit C.; Mukherjee, Sampad; Wu, Ying-Hai; Mandal, Sudhansu S.; Wójs, Arkadiusz; Cheianov, Vadim; Jain, J. K.

doi:10.1103/physrevb.95.125302

Cited by 21 publications

(25 citation statements)

References 66 publications

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“…The pair-correlation functions of both states show oscillations that decay at long distances, which is a typical characteristic of an incompressible state [62,63]. Moreover, both states show a "shoulder"-like feature in the pair-correlation function at short distances, which is a signature of clustering in non-Abelian states [13,64]. Furthermore, these two pair-correlation functions are in remarkably good agreement with each other.…”

Section: A Ground Statesupporting

confidence: 55%

Non-Abelian fractional quantum Hall state at 3/7 -filled Landau level

Faugno

Jain

Balram

2020

Phys. Rev. Research

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We consider a non-Abelian candidate state at filling factor ν = 3/7 state belonging to the parton family. We find that, in the second Landau level of GaAs (i.e., at filling factor ν = 2 + 3/7), this state is energetically superior to the standard Jain composite-fermion state and also provides a very good representation of the ground state found in exact diagonalization studies of finite systems. This leads us to predict that if a fractional quantum Hall effect is observed at ν = 3/7 in the second Landau level, it is likely to be described by this new non-Abelian state. We enumerate experimentally measurable properties that can verify the topological structure of this state.

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Section: A Ground Statesupporting

confidence: 55%

Non-Abelian fractional quantum Hall state at 3/7 -filled Landau level

Faugno

Jain

Balram

2020

Phys. Rev. Research

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“…55. We see a "shoulder"-like bump at short distances in the pair-correlation function which is considered to be a characteristic of non-Abelian states that involve clustering 10,12,14,56,57 . In this work we have introduced a parton wave function, denoted by Ψ22 111 1/2 , describing a FQH state in a half-filled Landau level that lies in the same phase as the anti-Pfaffian state.…”

Section: Applications and Extensionsmentioning

confidence: 94%

Parton construction of a wave function in the anti-Pfaffian phase

2018

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In this work we propose a parton state as a candidate state to describe the fractional quantum Hall effect in the half-filled second Landau level. The wave function for this parton state is PLLLΦ 3 1 [Φ * 2 ] 2 ∼ Ψ 2 2/3 /Φ1 and in the spherical geometry it occurs at the same flux as the anti-Pfaffian state. This state has a good overlap with the anti-Pfaffian state and with the ground state obtained by exact diagonalization, using the SLL Coulomb interaction pseudopotentials for an ordinary semiconductor such as GaAs. By calculating the entanglement spectrum we show that this state lies in the same phase as the anti-Pfaffian state. A major advantage of this parton state is that its wave function can be evaluated for large systems, which makes it amenable to variational calculations. In the appendix of this work we have numerically assessed the validity of another candidate state at 5/2, namely the particle-hole-symmetric Pfaffian (PH-Pfaffian) state. We find that the proposed candidate wave function for the PH-Pfaffian state is particle-hole symmetric to a high degree but it does not appear to arise as the ground state of any simple two-body Hamiltonian.

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“…Intriguingly, the n = 3 state of Eq. (5) provides a candidate ground-state wave function that could possibly describe the FQHE at 2 + 3/8 [11][12][13][14][15]61,62]. We thus speculate that then2 2 1 4 family of parton states may capture the observed plateaus at 2/5 and 3/8 in the SLL of GaAs [11][12][13][14][15] that were not covered in then21 3 sequence of Ref.…”

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confidence: 84%

Parton construction of particle-hole-conjugate Read-Rezayi parafermion fractional quantum Hall states and beyond

2019

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The Read-Rezayi (RR) parafermion states form a series of exotic non-Abelian fractional quantum Hall (FQH) states at filling ν = k/(k + 2). Computationally, the wave functions of these states are prohibitively expensive to generate for large systems. We introduce a series of parton states, denoted2 k 1 k+1 , and show that they lie in the same universality classes as the particle-hole-conjugate RR ("anti-RR") states. Our analytical results imply that a [U (1) k+1 × U (2k) −1 ]/[SU (k) −2 × U (1) −1 ] coset conformal field theory describes the edge excitations of the2 k 1 k+1 state, suggesting nontrivial dualities with respect to previously known descriptions. The parton construction allows wave functions in anti-RR phases to be generated for hundreds of particles. We further propose the parton sequencen2 2 1 4 , with n = 1, 2, 3, to describe the FQH states observed at ν = 2 + 1/2, 2 + 2/5, and 2 + 3/8.

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The enigma of theν=2+3/8fractional quantum Hall effect

Cited by 21 publications

References 66 publications

Non-Abelian fractional quantum Hall state at 3/7 -filled Landau level

Non-Abelian fractional quantum Hall state at 3/7 -filled Landau level

Parton construction of a wave function in the anti-Pfaffian phase

Parton construction of particle-hole-conjugate Read-Rezayi parafermion fractional quantum Hall states and beyond

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