A Conformal Field Theory Description of the Paired and Parafermionic States in the Quantum Hall Effect

Cristofano, Gerardo; Maiella, G.; Marotta, Vincenzo

doi:10.1142/s021773230000219x

Cited by 22 publications

(133 citation statements)

References 23 publications

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“…Note that for QH states with even-denominator d H the minimal electric charge is Q min = 1/(ld h ), where l is an even integer called the charge parameter -see Theorem 4.3 in [27]. A recent study of the MR state in the framework of the parafermionic FQH states [28,16,17], realized as coset constructions [11], has made the mechanism of clustering more transparent. In particular, the MR state is realized as an affine coset projection [11] su(2) 1 ⊕ su(2) 1 → su(2) 1 ⊕ su(2) 1 / su(2) 2 , in an abelian lattice theory of the type [11,27] (3| 1 A 1 1 A 1 ), i.e., a theory with a K-matrix and a charge vector Q…”

Section: The Moore-read State: the Cft Coset Point Of Viewmentioning

confidence: 99%

The ν=5/2 quantum Hall state revisited: spontaneous breaking of the chiral fermion parity and phase transition between Abelian and non-Abelian statistics

Georgiev

2003

Nuclear Physics B

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We review a recent development in the theoretical understanding of the ν = 5/2 quantum Hall plateau and propose a new conformal field theory, slightly different from the Moore-Read one, to describe another universality class relevant for this plateau. The ground state is still given by the Pfaffian and is completely polarized, however, the elementary quasiholes are charge 1/2 anyons with abelian statistics θ = π/2, which obey complete spin-charge separation. The physical hole is represented by two such quasiholes plus a free neutral Majorana fermion. We also compute the periods and amplitudes of the chiral persistent currents in both states and show that they have different temperature dependence. Finally, we find indications of a classical two-step phase transition between the new and the Moore-Read states, through a compressible state, which is characterized by the spontaneous breaking of a hidden Z 2 symmetry corresponding to the conservation of the chiral fermion parity. We believe that this transition could explain the "kink" observed in the activation experiment for ν = 5/2.

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Section: The Moore-read State: the Cft Coset Point Of Viewmentioning

confidence: 99%

The ν=5/2 quantum Hall state revisited: spontaneous breaking of the chiral fermion parity and phase transition between Abelian and non-Abelian statistics

Georgiev

2003

Nuclear Physics B

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“…The affine coset realization of the parafermions has a long history, please see Refs. [23][24][25] and the references in [8]. The primary fields of the coset (53) are labelled by [8] …”

Section: Remark 3 Note That F λ Are Always Real the Reason Is That Tmentioning

confidence: 99%

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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“…[1][2] are obtained and the transformations above coincide with the transformations given in eqs. (15) for δ = π 2 .…”

Section: The Tm Modelmentioning

confidence: 99%

“…[1][2]) can be conjectured to represent the correct CFT which describes dissipative quantum mechanics (DQM) of ref. [5].…”

Section: The Tm Modelmentioning

confidence: 99%

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A twisted conformal field theory description of dissipative quantum mechanics

2004

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We show how the recently proposed CFT for a bilayer Quantum Hall system at filling ν = m pm+2 [1]−[3], the Twisted Model (TM), is equivalent to the system of two massless scalar bosons with a magnetic boundary interaction as introduced in [4], at the so called "magic" points. We are then able to describe, within such a framework, the dissipative quantum mechanics of a particle confined to a plane and subject to an external magnetic field normal to it. Such an analogy is further developed in terms of the TM boundary states, by describing the interaction between an impurity with a Hall system.

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A Conformal Field Theory Description of the Paired and Parafermionic States in the Quantum Hall Effect

Cited by 22 publications

References 23 publications

The ν=5/2 quantum Hall state revisited: spontaneous breaking of the chiral fermion parity and phase transition between Abelian and non-Abelian statistics

The ν=5/2 quantum Hall state revisited: spontaneous breaking of the chiral fermion parity and phase transition between Abelian and non-Abelian statistics

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

A twisted conformal field theory description of dissipative quantum mechanics

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