Quantitative study of large composite-fermion systems

Jain, J. K.; Park, K.; Melik-Alaverdian, V.; Bonesteel, N. E.

doi:10.1103/physrevb.55.r4895

Cited by 208 publications

(194 citation statements)

References 6 publications

(8 reference statements)

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“…44 This form, while not strictly identical to the form of Eq. 3, is extremely close numerically and has equally impressive overlaps with exact diagonalizations 43 and is therefore an equally good starting point for studying composite fermion physics. However, in contrast to the form of Eq.…”

Section: A Composite Fermion Liquidmentioning

confidence: 99%

“…3 is exceedingly difficult to implement numerically for large systems. To circumvent this problem, Jain and Kamilla 43 proposed a rewriting of the composite fermion wavefunction as…”

Section: A Composite Fermion Liquidmentioning

confidence: 99%

“…6 and 7 are comparatively easy to evaluate numerically and therefore allow large system quantum Monte-Carlo calculations. 43 In this paper, we have used this type of approach. In order to obtain a wavefunction for the bilayer system at ν = 1 2 + 1 2 and infinite layer separation, a simple product state of two composite fermion liquids (CFL) is appropriate.…”

Section: A Composite Fermion Liquidmentioning

confidence: 99%

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Trial wave functions forν=12+12quantum Hall bilayers

Möller¹,

Simon²,

Rezayi

2009

Phys. Rev. B

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Quantum Hall bilayer systems at filling fractions near ν = 1 2 + 1 2 undergo a transition from a compressible phase with strong intralayer correlation to an incompressible phase with strong interlayer correlations as the layer separation d is reduced below some critical value. Deep in the intralayer phase (large separation) the system can be interpreted as a fluid of composite fermions (CFs), whereas deep in the interlayer phase (small separation) the system can be interpreted as a fluid of composite bosons (CBs). The focus of this paper is to understand the states that occur for intermediate layer separation by using trial variational wavefunctions. We consider two main classes of wavefunctions. In the first class, previously introduced in Möller et al. (2003)] and generalizes the idea of pairing wavefunctions by allowing the CFs also to be replaced continuously by CBs. This generalization allows us to construct exceedingly good wavefunctions for interlayer spacings of d ℓ 0 , as well. The accuracy of the wavefunctions discussed in this work, compared with exact diagonalization, approaches that of the celebrated Laughlin wavefunction.

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Section: A Composite Fermion Liquidmentioning

confidence: 99%

“…3 is exceedingly difficult to implement numerically for large systems. To circumvent this problem, Jain and Kamilla 43 proposed a rewriting of the composite fermion wavefunction as…”

Section: A Composite Fermion Liquidmentioning

confidence: 99%

Section: A Composite Fermion Liquidmentioning

confidence: 99%

See 1 more Smart Citation

Trial wave functions forν=12+12quantum Hall bilayers

Möller¹,

Simon²,

Rezayi

2009

Phys. Rev. B

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“…Incidentally, the bound state of the test boson and unit vortex is also a composite fermion.) The LLL projection will be evaluated by methods given in the literature [32,37]. Fig.…”

mentioning

confidence: 99%

Fractional Angular Momentum in Cold-Atom Systems

Zhang¹,

Sreejith²,

Gemelke³

et al. 2014

Phys. Rev. Lett.

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The quantum statistics of bosons or fermions are manifest through even or odd relative angular momentum of a pair. We show theoretically that, under certain conditions, a pair of certain test particles immersed in a fractional quantum Hall state possesses, effectively, a fractional relative angular momentum, which can be interpreted in terms of fractional braid statistics. We propose that the fractionalization of the angular momentum can be detected directly through the measurement of the pair correlation function in rotating ultra-cold atomic systems in the fractional quantum Hall regime. Such a measurement will also provide direct evidence for the effective magnetic field resulting from Berry phases arising from attached vortices, and of excitations with fractional particle number, analogous to fractional charge of electron fractional quantum Hall effect.PACS numbers: 03.65. Vf,03.75.Mn, While all particles in nature are either bosons or fermions, emergent particles in strongly correlated condensed matter systems can, in principle, obey fractional braid statistics [1,2], which refers to the property that their braiding produces phases that are non-integral multiples of 2π. It was proposed three decades ago [3,4] that the fractional quantum Hall effect [5] (FQHE) provides a platform for the realization of such entities. No convincing measurement of the fractional braid statistics has yet been made. In this Letter we consider a pair of test atoms in a background FQHE state of bosonic atoms. Under certain conditions, the test atoms capture vortices and the bound states of atoms and vortices behave effectively as particles with fractional braid statistics. Just as fermionic or bosonic statistics are reflected through an odd or even integer relative angular momentum for a pair of particles, fractional braid statistics are manifest through fractional relative angular momentum. We further show that the relative angular momentum can be deduced from the pair correlation function through determination of the radii of various quantized orbits of one test particle around another. This provides a method for measuring fractional braid statistics relying only on already existing experimental methods of introducing test atoms as well as of measuring their pair correlation function in ultra-cold bosons in rapidly rotating optical traps. No direct interferometric or phase measurement is necessary. In addition, our proposed experiment will provide a direct measurement of the effective magnetic field arising from a binding of vortices to bosons, as well as of excitations involving a fraction of a boson.Neutral bosons can in principle be driven into the FQHE regime by rapid rotation, which effectively amounts to application of a magnetic field. The strongly interacting regime is reached as the number of vortices (N V ) in a rotating Bose-Einstein condensate becomes comparable with the number of atoms N , which is parametrized by the filling factor ν = N/N V . Various methods have been developed for producing vorticity in atomic Bo...

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“…1, we show a comparison for a larger range of λ for ν = 1/3, 2/5, and 3/7. The reader is referred to the literature for the details of the variational Monte Carlo methods used for evaluating the gaps from the CF wave functions 24,23 . The MS gap does not work at small λ, as expected, since here the energetics is controlled by the large q terms in the Hamiltonian, which have been neglected in the above MS analysis.…”

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confidence: 99%

Scaling relations for gaps in fractional quantum Hall states

et al. 1998

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The microscopic Hamiltonian approach of Murthy and Shankar, which has recently been used to calculate the transport gaps of quantum Hall states with fractions ν = p 2ps+1, also implies scaling relations between gaps within a single sequence (fixed s) as well as between gaps of corresponding states in different sequences. This work tests these relations for a system of electrons in the lowest Landau level interacting with a model potential cutoff at high momenta due to sample thickness.

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Quantitative study of large composite-fermion systems

Cited by 208 publications

References 6 publications

Trial wave functions forν=12+12quantum Hall bilayers

Trial wave functions forν=12+12quantum Hall bilayers

Fractional Angular Momentum in Cold-Atom Systems

Scaling relations for gaps in fractional quantum Hall states

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