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Quantum Hall quasielectron operators in conformal field theory
Stockholm University, Faculty of Science, Department of Physics.
Stockholm University, Faculty of Science, Department of Physics.
2009 (English)In: Physical Review B Condensed Matter, ISSN 0163-1829, E-ISSN 1095-3795, Vol. 80, no 16, 165330-1-165330-22 p.Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
American Physical Society , 2009. Vol. 80, no 16, 165330-1-165330-22 p.
National Category
Physical Sciences
Identifiers
URN: urn:nbn:se:su:diva-37222DOI: 10.1103/PhysRevB.80.165330ISI: 000271352100105OAI: oai:DiVA.org:su-37222DiVA: diva2:295429
Available from: 2010-02-17 Created: 2010-02-17 Last updated: 2017-12-12Bibliographically approved
In thesis
1. Quasielectrons in Abelian and non-Abelian Quantum Hall States
Open this publication in new window or tab >>Quasielectrons in Abelian and non-Abelian Quantum Hall States
2010 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Strongly correlated electron systems continue to  attract a lot of interest. Especially two-dimensional electron systems have shown many surprising behaviours. A fascinating example is the quantum Hall effect, which arises when electrons are confined to two dimensions, subjected to a very large magnetic field, and cooled to very low temperatures. Under these conditions, the electrons form new states of matter - the strongly correlated quantum Hall liquids. A hallmark of these quantum liquids is the precise quantization of the Hall conductance, but in recent years more attention has been focused on their exotic excitations. These have fractional electric charge, and fractional exchange statistics. The latter implies that the wave function is multiplied by a phase factor containing a fractional phase when two quasiparticles are moved around each other. Thus, they are neither bosons nor fermions, but so-called anyons. In recent years, there has accumulated theoretical and experimental evidence  for some of the quantum Hall liquids having even more exotic excitations with not only fractional but non-Abelian exchange statistics. The quasiparticles of such systems could be used to build topologically protected quantum bits, which are much more robust than presently available quantum bits; they would be the ideal building blocks of a quantum computer.

 We use conformal field theory to describe the quantum Hall liquids, as well as their excitations. In particular, we represent the electrons and quasiparticles by conformal field theory operators. Even though the operator description for quasiholes is very well understood, it was for a long time unclear how to describe their antiparticles, the quasielectrons. We found an operator  that describes quasielectron excitations correctly and shares many of the useful properties of the corresponding quasihole operator. For instance, many of the topological properties of the particles are manifest in the operator. This not only adds a missing piece to the quantum Hall puzzle,  but it also opens up new and exciting possibilities. For instance, we were able to extend this construction to the non-Abelian states. A highly non-trivial application of our approach is the condensation of non-Abelian quasielectrons, which yields new non-Abelian quantum Hall states with non-Abelian properties that differ from those of their parent states.

Place, publisher, year, edition, pages
Stockholm: Department of Physics, Stockholm University, 2010. 62 p.
Keyword
quantum Hall effect
National Category
Condensed Matter Physics
Research subject
Theoretical Physics
Identifiers
urn:nbn:se:su:diva-37203 (URN)978-91-7447-016-1 (ISBN)
Public defence
2010-03-30, FB52, AlbaNova University Center, Roslagstullsbacken 21, Stockholm, 10:00 (English)
Opponent
Supervisors
Available from: 2010-03-08 Created: 2010-02-17 Last updated: 2010-02-24Bibliographically approved

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