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Nontrivial ground-state degeneracies and generalized fractional excitations in the 1D lattice
Stockholm University, Faculty of Science, Department of Physics.
(English)Manuscript (preprint) (Other academic)
Abstract [en]

We study a 1D lattice Hamiltonian, relevant for a wide range of interesting physical systems like, e.g., the quantum-Hall system, cold atoms or molecules in optical lattices, and TCNQ salts. Through a tuning of the interaction parameters and a departure from a strictly convex interaction, nontrivial ground-state degeneracies and fractionally charged excitations emerge. The excitations, being a generalization of the fractional charges known from the fractional quantum-Hall effect, appear as domain walls between inequivalent ground states and carry the charge ± e/mq , where m is an integer and associated with the specified interaction, and ν = p/q is the filling fraction in the lattice. The description points at an interesting resemblance to states connected to non-Abelian statistics, which is central for the concept of topological quantum computing. 

National Category
Physical Sciences
Research subject
Theoretical Physics
Identifiers
URN: urn:nbn:se:su:diva-89416OAI: oai:DiVA.org:su-89416DiVA: diva2:617855
Available from: 2013-04-24 Created: 2013-04-24 Last updated: 2013-05-02Bibliographically 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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