| 1. |
- Tournois, Yoran, 1991-
(författare)
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Abelian and non-abelian quantum Hall hierarchies
- 2020
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- A core tenet of condensed matter physics has been that different phases of matter can be classified according to Landau's symmetry breaking paradigm. It has become clear, however, that phases of matter exist that are not distinguished by symmetry, but rather by topology. A paradigmatic example of this topological order are the fractional quantum Hall phases, which are the topic of this dissertation. Such phases exhibit the fractional quantum Hall effect, which occurs when electrons confined to two dimensions are subjected to a strong perpendicular magnetic field at very low temperatures. Characterized by a precise quantization of the Hall resistance and a concomitant vanishing of the longitudinal resistance, the fractional quantum Hall effect results from the formation of a strongly correlated quantum liquid of electrons. This quantum liquid supports remarkable quasiparticle excitations, which carry a fractional charge and are thought to obey fractional statistics beyond the familiar Bose-Einstein and Fermi-Dirac statistics.The theoretical understanding of the topological orders realized by the fractional quantum Hall states has progressed by the proposal of explicit trial wave functions as well as various types of effective field theories. This dissertation focuses on two series of trial wave functions, abelian and non-abelian hierarchy wave functions. We study the non-abelian hierarchy wave functions using conformal field theory techniques, by means of which the associated topological properties are studied. These include the fractional charges of the quasiparticles and their non-abelian fractional statistics. In addition, we study abelian hierarchy wave functions using effective Ginzburg-Landau theories in a way that connects to their known conformal field theory description.
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| 2. |
- Tournois, Yoran, et al.
(författare)
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Braiding properties of paired spin-singlet and non-Abelian hierarchy states
- 2020
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Ingår i: Journal of Physics A. - : IOP Publishing. - 1751-8113 .- 1751-8121. ; 53:5
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Tidskriftsartikel (refereegranskat)abstract
- We study explicit model wave functions describing the fundamental quasiholes in a class of non-Abelian fractional quantum Hall states. This class is a family of paired spin-singlet states with n ⩾ 1 internal degrees of freedom. We determine the braid statistics of the quasiholes by determining the monodromy of the explicit quasihole wave functions, that is how they transform under exchanges of quasihole coordinates. The statistics is shown to be the same as that of the quasiholes in the Read–Rezayi states, up to a phase. We also discuss the application of this result to a class of non-Abelian hierarchy wave functions.
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| 3. |
- Tournois, Yoran, et al.
(författare)
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Conformal field theory construction for non-Abelian hierarchy wave functions
- 2017
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Ingår i: Physical Review B. - : American Physical Society (APS). - 2469-9950 .- 2469-9969. ; 96:24
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Tidskriftsartikel (refereegranskat)abstract
- The fractional quantum Hall effect is the paradigmatic example of topologically ordered phases. One of its most fascinating aspects is the large variety of different topological orders that may be realized, in particular non-Abelian ones. Here we analyze a class of non-Abelian fractional quantum Hall model states which are generalizations of the Abelian Haldane-Halperin hierarchy. We derive their topological properties and show that the quasiparticles obey non-Abelian fusion rules of type su(q)k. For a subset of these states we are able to derive the conformal field theory description that makes the topological properties—in particular braiding—of the state manifest. The model states we study provide explicit wave functions for a large variety of interesting topological orders, which may be relevant for certain fractional quantum Hall states observed in the first excited Landau level.
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| 4. |
- Tournois, Yoran, et al.
(författare)
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Microscopic derivation of Ginzburg-Landau theories for hierarchical quantum Hall states
- 2020
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Ingår i: SciPost Physics. - : SCIPOST FOUNDATION. - 2542-4653. ; 8:5
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Tidskriftsartikel (refereegranskat)abstract
- We propose a Ginzburg-Landau theory for a large and important part of the abelian quantum Hall hierarchy, including the prominently observed Jain sequences. By a generalized "flux attachment" construction we extend the Ginzburg-Landau-Chern-Simons composite boson theory to states obtained by both quasielectron and quasihole condensation, and express the corresponding wave functions as correlators in conformal field theories. This yields a precise identification of the relativistic scalar fields entering these correlators in terms of the original electron field.
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