Non-abelian quantum Hall states and fractional charges in one dimension
2013 (English)Doctoral thesis, comprehensive summary (Other academic)
The fractional quantum Hall effect has, since its discovery around 30 years ago, been a vivid field of research—both experimentally and theoretically. In this thesis we investigate certain non-abelian quantum Hall states by mapping the two-dimensional system onto a thin torus, where the problem becomes effectively one-dimensional and hopping is suppressed, meaning that the classical electrostatic interaction dominates. The approach assists with a simplified view of ground states and their degeneracies, as well as of the nature of the fractionally charged, minimal excitations of the corresponding quantum Hall states. Similar models are also relevant for cold atoms trapped in one-dimensional optical lattices, where interaction parameters are available for tuning, which opens up for realizing interesting lattice states in controllable environments. The diverse applicability of the one-dimensional electrostatic lattice hamiltonian motivates the exploration of the systems and models treated in this work.
In the absence of hopping or tunneling, the low-energy behavior of the one-dimensional lattice system is ultimately dependent on the nature of the electrostatic interaction present. For ordinary interactions such as Coulomb, the ground state at particle filling fraction ν= p/q has a well-known q-fold center-of-mass degeneracy and the elementary excitations are domain walls of fractional charge e* = ±e/q. These appear in abelian quantum Hall systems and are known since earlier. In this work, we show how other types of interaction give rise to increased ground state degeneracies and, as a result, to the emergence of split fractional charges recognized from non- abelian quantum Hall systems.
Place, publisher, year, edition, pages
Stockholm: Department of Physics, Stockholm University , 2013. , 72 p.
Physical Sciences Condensed Matter Physics
Research subject Theoretical Physics
IdentifiersURN: urn:nbn:se:su:diva-89417ISBN: 978-91-7447-714-6OAI: oai:DiVA.org:su-89417DiVA: diva2:617865
2013-06-04, FB42, AlbaNova universitetscentrum, Roslagstullsbacken 21, Stockholm, 14:00 (English)
Langmann, Edwin, Professor
Karlhede, Anders, Professor
At the time of the doctoral defense, the following paper was unpublished and had a status as follows: Paper 5: Manuscript.2013-05-132013-04-242013-06-10Bibliographically approved
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