| 1. |
- Bergholtz, Emil Johansson, et al.
(författare)
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Microscopic theory of the quantum Hall hierarchy
- 2007
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Ingår i: Physical Review Letters. - 0031-9007 .- 1079-7114. ; 99:25, s. 256803-1-256803-4
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Tidskriftsartikel (refereegranskat)abstract
- We solve the quantum Hall problem exactly in a limit and show that the ground states can be organized in a fractal pattern consistent with the Haldane-Halperin hierarchy, and with the global phase diagram. We present wave functions for a large family of states, including those of Laughlin and Jain and also for states recently observed by Pan et al., and show that they coincide with the exact ones in the solvable limit. We submit that they establish an adiabatic continuation of our exact results to the experimentally accessible regime, thus providing a unified approach to the hierarchy states.
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| 2. |
- Bergholtz, Emil Johansson, et al.
(författare)
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Quantum Hall hierarchy wave functions: From conformal correlators to Tao-Thouless states
- 2008
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Ingår i: Physical Review B Condensed Matter. - 0163-1829 .- 1095-3795. ; 77:16, s. 165325-1-165325-9
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Tidskriftsartikel (refereegranskat)abstract
- Laughlin’s wave functions, which describe the fractional quantum Hall effect at filling factorsν=1/(2k+1), can be obtained as correlation functions in a conformal field theory, and recently, this construction was extended to Jain’s composite fermion wave functions at filling factors ν=n/(2kn+1). Here, we generalize this latter construction and present ground state wave functions for all quantum Hall hierarchy states that are obtained by successive condensation of quasielectrons (as opposed to quasiholes) in the original hierarchy construction. By considering these wave functions on a cylinder, we show that they approach the exact ground states, which are the Tao-Thouless states, when the cylinder becomes thin. We also present wave functions for the multihole states, make the connection to Wen’s general classification of Abelian quantum Hall fluids, and discuss whether the fractional statistics of the quasiparticles can be analytically determined. Finally, we discuss to what extent our wave functions can be described in the language of composite fermions.
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| 3. |
- Hansson, Thors Hans, et al.
(författare)
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Conformal Field Theory Approach to Abelian and Non-Abelian Quantum Hall Quasielectrons
- 2009
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Ingår i: Physical Review Letters. - : American Physical Society. - 0031-9007 .- 1079-7114. ; 102:16, s. 166805-1-166805-4
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Tidskriftsartikel (refereegranskat)abstract
- The quasiparticles in quantum Hall liquids carry fractional charge and obey fractional quantum statistics. Of particular recent interest are those with non-Abelian statistics, since their braiding properties could, in principle, be used for robust coding of quantum information. There is already a good theoretical understanding of quasiholes in both Abelian and non-Abelian quantum Hall states. Here we develop conformal field theory methods that allow for an equally precise description of quasielectrons and explicitly construct two- and four-quasielectron excitations of the non-Abelian Moore-Read state.
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| 4. |
- Hansson, Thors Hans, et al.
(författare)
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Quantum Hall quasielectron operators in conformal field theory
- 2009
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Ingår i: Physical Review B Condensed Matter. - : American Physical Society. - 0163-1829 .- 1095-3795. ; 80:16, s. 165330-1-165330-22
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Tidskriftsartikel (refereegranskat)abstract
- In the conformal field theory (CFT) approach to the quantum Hall effect, the multielectron wave functions are expressed as correlation functions in certain rational CFTs. While this approach has led to a well-understood description of the fractionally charged quasihole excitations, the quasielectrons have turned out to be much harder to handle. In particular, forming quasielectron states requires nonlocal operators, in sharp contrast to quasiholes that can be created by local chiral vertex operators. In both cases, the operators are strongly constrained by general requirements of symmetry, braiding, and fusion. Here we construct a quasielectron operator satisfying these demands and show that it reproduces known good quasiparticle wave functions, as well as predicts additional ones. In particular, we propose explicit wave functions for quasielectron excitations of the Moore-Read Pfaffian state. Further, this operator allows us to explicitly express the composite fermion wave functions in the positive Jain series in hierarchical form, thus settling a long-time controversy. We also critically discuss the status of the fractional statistics of quasiparticles in the Abelian hierarchical quantum Hall states and argue that our construction of localized quasielectron states sheds new light on their statistics. At the technical level we introduce a generalized normal ordering that allows us to “fuse” an electron operator with the inverse of an hole operator and also an alternative approach to the background charge needed to neutralize CFT correlators. As a result we get a fully holomorphic CFT representation of a large set of quantum Hall wave functions.
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| 5. |
- Hermanns, Maria, et al.
(författare)
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Quantum Hall wave functions on the torus
- 2008
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Ingår i: Physical Review B Condensed Matter. - : American Physical Society. - 0163-1829 .- 1095-3795. ; 77:12, s. 125321-1-125321-16
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Tidskriftsartikel (refereegranskat)abstract
- We present explicit expressions for a large set of hierarchy wave functions on the torus. Included are the Laughlin states, the states in the positive Jain series, and recently observed states at, e.g., ν=4∕11. The techniques we use constitute a nontrivial extension of the conformal field theory methods developed earlier to construct the corresponding wave functions in disk geometry.
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