Fradkin and Hisle share plans for ACRL

Fradkin, Bernard; Hisle, W. Lee

doi:10.5860/crln.57.3.151

Cited by 2 publications

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“…Since the ground state degeneracies were not calculated, the relation between the effective theories in Ref. [18] and the effective theories obtained in this paper is unclear at the moment.…”

Section: Introductionmentioning

confidence: 79%

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Projective construction of non-Abelian quantum Hall liquids

1999

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Using projective construction, a generalized parton construction, we construct many non-Abelian quantum Hall (QH) states, which include the Pfaffian state at filling fraction ν = 1/2. The projective construction allows us to calculate the bulk and the edge effective theory for the constructed QH state. We illustrate how to use the bulk effective theory to calculate the ground state degeneracy of non-Abelian QH liquids on torus. We point out that the full description of the effective theory requires both the effective Lagrangian and the definition of electron operators. The latter generates all physical states and defines the gauge structure of the theory.

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Section: Introductionmentioning

confidence: 79%

“…Another form of effective theory -the non-Abelian Ginzburg-Landau CS theory -was obtained in Ref. [18] to describe the Pfaffian states. Since the ground state degeneracies were not calculated, the relation between the effective theories in Ref.…”

Section: Introductionmentioning

confidence: 99%

Projective construction of non-Abelian quantum Hall liquids

1999

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“…In these cases, we have simply recovered known constructions of these algebras and representations from the parafermions [25,33]. The special cases k = 1 (the Laughlin state) and k = 2 (the Pfaffian state) of these were mentioned earlier [16,20], and the SU(2) k = 2, M = 0 case was used in a recent paper [34].…”

Section: (220)mentioning

confidence: 99%

Beyond paired quantum Hall states: Parafermions and incompressible states in the first excited Landau level

1999

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The Pfaffian quantum Hall states, which can be viewed as involving pairing either of spinpolarized electrons or of composite fermions, are generalized by finding the exact ground states of certain Hamiltonians with k + 1-body interactions, for all integers k ≥ 1. The remarkably simple wavefunctions of these states involve clusters of k particles, and are related to correlators of parafermion currents in two-dimensional conformal field theory. The k = 2 case is the Pfaffian. For k ≥ 2, the quasiparticle excitations of these systems are expected to possess nonabelian statistics, like those of the Pfaffian. For k = 3, these ground states have large overlaps with the ground states of the (2-body) Coulomb-interaction Hamiltonian for electrons in the first excited Landau level at total filling factors ν = 2 + 3/5, 2 + 2/5.

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Fradkin and Hisle share plans for ACRL

Cited by 2 publications

References 0 publications

Projective construction of non-Abelian quantum Hall liquids

Projective construction of non-Abelian quantum Hall liquids

Beyond paired quantum Hall states: Parafermions and incompressible states in the first excited Landau level

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