| 1. |
- Bergholtz, Emil J, et al.
(författare)
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Half-filled lowest Landau level on a thin torus.
- 2005
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Ingår i: Phys Rev Lett. - 0031-9007. ; 94:2, s. 026802-
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Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)abstract
- We solve a model that describes an interacting electron gas in the half-filled lowest Landau level on a thin torus, with radius of the order of the magnetic length. The low-energy sector consists of noninteracting, one-dimensional, neutral fermions. The ground state, which is homogeneous, is the Fermi sea obtained by filling the negative energy states, and the excited states are gapless neutral excitations out of this one-dimensional sea. Although the limit considered is extreme, the solution has a striking resemblance to the composite fermion description of the bulk \nu = 1/2 state—the ground state is homogeneous and the excitations are neutral and gapless. This suggests a one-dimensional Luttinger liquid description, with possible observable effects in transport experiments, of the bulk state where it develops continuously from the state on a thin torus as the radius increases.
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| 2. |
- 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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| 3. |
- Bergholtz, Emil J, et al.
(författare)
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'One-dimensional' theory of the quantum Hall system
- 2006
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Ingår i: Journal of Statistical Mechanics: Theory and Experiment. ; :L04001
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Tidskriftsartikel (refereegranskat)abstract
- We consider the lowest Landau level on a torus as a function of its circumference L_1. When L_1 → 0, the ground state at general rational filling fraction is a crystal with a gap—a Tao–Thouless state. For filling fractions ν = p/(2pm + 1), these states are the limits of Laughlin's or Jain's wavefunctions describing the gapped quantum Hall states when L_1 → ∞. For the half-filled Landau level, there is a transition to a Fermi sea of non-interacting neutral fermions (dipoles), or rather to a Luttinger liquid modification thereof, at L_1 ~ 5 magnetic lengths. Using exact diagonalization we identify this state as a version of the Rezayi–Read state, and find that it develops continuously into the state that is believed to describe the observed metallic phase as L_1 → ∞. Furthermore, the effective Landau level structure that emerges within the lowest Landau level is found to be a consequence of the magnetic symmetries.
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| 4. |
- Bergholtz, E. J., et al.
(författare)
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Pfaffian quantum Hall state made simple : Multiple vacua and domain walls on a thin torus
- 2006
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Ingår i: Physical Review B. Condensed Matter and Materials Physics. - 1098-0121 .- 1550-235X. ; 74:8, s. 081308-
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Tidskriftsartikel (refereegranskat)abstract
- We analyze the Moore-Read Pfaffian state on a thin torus. The known sixfold degeneracy is realized by two inequivalent crystalline states with a four- and twofold degeneracy, respectively. The fundamental quasihole and quasiparticle excitations are domain walls between these vacua, and simple counting arguments give a Hilbert space of dimension 2n−1 for 2n−k holes and k particles at fixed positions and assign each a charge ±e∕4. This generalizes the known properties of the hole excitations in the Pfaffian state as deduced using conformal field theory techniques. Numerical calculations using a model Hamiltonian and a small number of particles support the presence of a stable phase with degenerate vacua and quarter-charged domain walls also away from the thin-torus limit. A spin-chain Hamiltonian encodes the degenerate vacua and the various domain walls.
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| 5. |
- 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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| 6. |
- Bergholtz, Emil, et al.
(författare)
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Quantum Hall Circle
- 2009
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Ingår i: Journal of Statistical Mechanics: Theory and Experiment. - : IOP. - 1742-5468. ; P04015
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Tidskriftsartikel (refereegranskat)abstract
- We consider spin-polarized electrons in a single Landau level on a cylinder as the circumference of the cylinder goes to infinity. This gives a model of interacting electrons on a circle where the momenta of the particles are restricted and there is no kinetic energy. Quantum Hall states are exact ground states for appropriate short range interactions, and there is a gap to excitations. These states develop adiabatically from this one-dimensional quantum Hall circle to the bulk quantum Hall states and further on into the Tao–Thouless states as the circumference goes to zero. For low filling fractions a gapless state is formed which we suggest is connected to the Wigner crystal expected in the bulk.
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| 7. |
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| 8. |
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| 9. |
- Hansson, T. H., et al.
(författare)
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Topological field theory for p-wave superconductors
- 2012
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Ingår i: New Journal of Physics. - : IOP Publishing. - 1367-2630. ; 14, s. 063017-
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Tidskriftsartikel (refereegranskat)abstract
- We propose a topological field theory for a spinless two-dimensional (2D) chiral superconductor (SC) that contains fundamental Majorana fields. Due to a fermionic gauge symmetry, the Majorana modes survive as dynamical degrees of freedom only at magnetic vortex cores, and on edges. We argue that these modes have the topological properties pertinent to a p-wave SC including the non-Abelian braiding statistics, and we support this claim by calculating the ground state degeneracy on a torus. We also briefly discuss the connection to the Moore-Read Pfaffian quantum Hall state and extensions to the spinfull case and to 3D topological SCs.
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| 10. |
- 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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