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Spin chain description of rotating bosons at v = 1
Stockholm University, Faculty of Science, Department of Physics.
Stockholm University, Faculty of Science, Department of Physics.
2009 (English)In: Journal of Statistical Mechanics: Theory and Experiment, ISSN 1742-5468, E-ISSN 1742-5468, P07038- p.Article in journal (Refereed) Published
Abstract [en]

We consider bosons at Landau level filling ν = 1 on a thin torus. In analogy with previous work on fermions at filling ν = 1/2, we map the low-energy sector onto a spin-1/2 chain. While the fermionic system may realize the gapless XY phase, we show that typically this does not happen for the bosonic system. Instead, both delta function and Coulomb interaction lead to gapped phases in the bosonic system, and in particular we identify a phase corresponding to the non-Abelian Moore–Read state. In the spin language, the Hamiltonian is dominated by a ferromagnetic next-nearest-neighbor interaction, which leads to a description consistent with the non-trivial degeneracies of the ground and excited states of this phase of matter. In addition we comment on the similarities and differences of the two systems mentioned above and fermions at ν = 5/2.

Place, publisher, year, edition, pages
2009. P07038- p.
Keyword [en]
solvable lattice models, fractional QHE (theory), spin chains, ladders and planes (theory), Bose Einstein condensation (theory)
National Category
Physical Sciences
Research subject
Theoretical Physics
Identifiers
URN: urn:nbn:se:su:diva-33309DOI: 10.1088/1742-5468/2009/07/L07003ISI: 000269353300038OAI: oai:DiVA.org:su-33309DiVA: diva2:282973
Available from: 2009-12-22 Created: 2009-12-22 Last updated: 2017-12-12Bibliographically approved
In thesis
1. Non-abelian quantum Hall states and fractional charges in one dimension
Open this publication in new window or tab >>Non-abelian quantum Hall states and fractional charges in one dimension
2013 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

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.
National Category
Physical Sciences Condensed Matter Physics
Research subject
Theoretical Physics
Identifiers
urn:nbn:se:su:diva-89417 (URN)978-91-7447-714-6 (ISBN)
Public defence
2013-06-04, FB42, AlbaNova universitetscentrum, Roslagstullsbacken 21, Stockholm, 14:00 (English)
Opponent
Supervisors
Note

At the time of the doctoral defense, the following paper was unpublished and had a status as follows: Paper 5: Manuscript.

Available from: 2013-05-13 Created: 2013-04-24 Last updated: 2013-06-10Bibliographically approved

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