A classification of quantum Hall fluids

Fröhlich, Jürg; Studer, Urban M.; Thiran, E.

doi:10.1007/bf02199122

Cited by 51 publications

(167 citation statements)

References 49 publications

(243 reference statements)

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“…The Gram matrix (12) implies that the topological charge q el of the electron should take the form [2] …”

Section: The Electron Charge Decompositionmentioning

confidence: 99%

“…Two of the assumptions in the CFT approach to the FQH effect, based on the FQH phenomenology, are that there is a minimal electric charge in the quasiparticle spectrum depending on the filling factor and there are only a finite number of topologically distinct quasiparticles [2]. This means that the CFT describing the FQH states should be rational.…”

Section: Laughlin's Spectral Flow and Cappelli-zemba Factorsmentioning

confidence: 99%

“…(49), using the approximation ln(1 + X) ≃ X for X ≪ 1 and taking the derivative with respect to φ according to Eq. (68) we get the following high-temperature asymptotic expression for the persistent current (note that 2π 2 …”

Section: High-temperature Asymptotics Of the Persistent Currents In Tmentioning

confidence: 99%

“…Because (µ, µ ′ ; µ ′′ ) def = (Λ µ , Λ µ ′ ; Λ α + Λ β ) we can shift the summation variables in the LHS according to µ = µ + µ ′ , α = α + µ ′ , β = β + µ ′ and use the triples equivalence (Λ µ , Λ µ ′ ; Λ α + Λ β ) ≡ (Λ µ , 0; Λ α + Λ β ) to get for the LHS µ ′ mod k µ mod k α≤ β P( µ, 0; α + β) S (1) Λ, µ+µ ′ S (1) Λ ′ ,µ ′ (S (2) α+µ ′ + β+µ ′ ,ν ) −1 ch µ , 0 α + β (τ),…”

Section: B the Diagonal Coset's S Matrixmentioning

confidence: 99%

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A universal conformal field theory approach to the chiral persistent currents in the mesoscopic fractional quantum Hall states

Georgiev

2005

Nuclear Physics B

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We propose a general and compact scheme for the computation of the periods and amplitudes of the chiral persistent currents, magnetizations and magnetic susceptibilities in mesoscopic fractional quantum Hall disk samples threaded by Aharonov-Bohm magnetic field. This universal approach uses the effective conformal field theory for the edge states in the quantum Hall effect to derive explicit formulas for the corresponding partition functions in presence of flux. We point out the crucial role of a special invariance condition for the partition function, following from the Bloch-Byers-Yang theorem, which represents the Laughlin spectral flow. As an example we apply this procedure to the Z k parafermion Hall states and show that they have universal non-Fermi liquid behavior without anomalous oscillations. For the analysis of the high-temperature asymptotics of the persistent currents in the parafermion states we derive the modular S -matrices constructed from the S matrices for the u(1) sector and that for the neutral parafermion sector which is realized as a diagonal affine coset.

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“…The Gram matrix (12) implies that the topological charge q el of the electron should take the form [2] …”

Section: The Electron Charge Decompositionmentioning

confidence: 99%

Section: Laughlin's Spectral Flow and Cappelli-zemba Factorsmentioning

confidence: 99%

Section: High-temperature Asymptotics Of the Persistent Currents In Tmentioning

confidence: 99%

Section: B the Diagonal Coset's S Matrixmentioning

confidence: 99%

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A universal conformal field theory approach to the chiral persistent currents in the mesoscopic fractional quantum Hall states

Georgiev

2005

Nuclear Physics B

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“…Complicated theories with very rich spectra of quasi-partilces, large central charge and large scaling dimension of electron operators may be unstable e.g. against formation of a Wigner-crystal [10].…”

mentioning

confidence: 99%

Effective-field theories for theν=52quantum Hall edge state

Boyarsky¹,

Cheianov

Fröhlich³

2009

Phys. Rev. B

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We present a list of possible effective theories which may describe a QHE edge at filling fraction ν = 5/2. We show that there exist several abelian and non-abelian effective theories (apart from those discussed in the literature) compatible with the physical requirements imposed by the microscopic nature of the system. We compare predictions of these theories with previous proposals and with the results of recent experiments. We identify a set of theories, both abelian and non-abelian, that cannot be distinguished based on the quasihole tunneling data only. We discuss what experimental information may be useful in resolving the ambiguity.PACS numbers: 03.65.Yz, 85.35.Ds One of the most striking predictions of the theory of the fractional quantum Hall effect is that a twodimensional electron gas in a strong magnetic field may exhibit a ground state supporting excitations (quasiparticles) with non-abelian braid statistics. In particular, Wen [1] and Moore and Read [2] have brought forward arguments attempting to explain the ν = 5/2 conductance plateau as a manifestation of such a "nonabelian" state. Not only is this possibility fascinating from the theoretical point of view, it also holds promise for concrete implementations of topologically protected quantum algorithms [3].Among non-abelian quantum Hall states, perhaps the simplest is the Moore-Read (Pfaffian) state, which has a simple intuitive interpretation as a p-wave paired state of composite fermions. The intuitive appeal of the MooreRead state does, however, not give a compelling clue as to its microscopic justification. The Hamiltonian of the many-electron system in a strong magnetic field is not amenable to a well-controlled perturbative treatment, whether in the electron or in the composite-fermion basis. Exact diagonalization numerical studies do not allow one to make fully reliable statements about macroscopically large systems. In this situation the decisive word about the nature of the ν = 5/2 state must come from experiments. A natural target for experimental investigations is the edge of an incompressible quantum Hall fluid supporting gapless excitations, including electric currents, and fractionally charged quasi-holes.In a recent experiment [4], properties of the ν = 5/2 state were investigated by means of a transport measurement in a quantum Hall sample with a narrow constriction. The parameters of the constriction were tuned in such a way that it served as a weak link between two ν = 5/2 quantum Hall edges. The electrical conductance of the constriction exhibits a zero bias peak, whose scaling with temperature is consistent with the assumption that the current is due to weak tunneling of fractionally charged quasi-particles. By fitting the shape of the zero-bias conductance peak to the predictions of a model-independent theory [6] at five different temperatures the experimentalists produced a two-parameter confidence map for the electric charge e * and the scaling dimension, g, of the most relevant (in the renormalization group sense) qua...

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Topological Quantum Computation with Non-Abelian Anyons in Fractional Quantum Hall States

Georgiev

2017

Quantum Systems in Physics, Chemistry, and Biology

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We review the general strategy of topologically protected quantum information processing based on non-Abelian anyons, in which quantum information is encoded into the fusion channels of pairs of anyons and in fusion paths for multi-anyon states, realized in two-dimensional fractional quantum Hall systems. The quantum gates which are needed for the quantum information processing in these multi-qubit registers are implemented by exchange or braiding of the nonAbelian anyons that are at fixed positions in two-dimensional coordinate space. As an example we consider the Pfaffian topological quantum computer based on the fractional quantum Hall state with filling factor ν H = 5/2. The elementary qubits are constructed by localizing Ising anyons on fractional quantum Hall antidots and various quantum gates, such as the Hadamard gate, phase gates and CNOT, are explicitly realized by braiding. We also discuss the appropriate experimental signatures which could eventually be used to detect non-Abelian anyons in Coulomb blockaded quantum Hall islands.

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A classification of quantum Hall fluids

Cited by 51 publications

References 49 publications

A universal conformal field theory approach to the chiral persistent currents in the mesoscopic fractional quantum Hall states

A universal conformal field theory approach to the chiral persistent currents in the mesoscopic fractional quantum Hall states

Effective-field theories for theν=52quantum Hall edge state

Topological Quantum Computation with Non-Abelian Anyons in Fractional Quantum Hall States

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