Dresden 2009 – wissenschaftliches Programm
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TT: Fachverband Tiefe Temperaturen
TT 42: Correlated Electrons: Low-dimensional Systems - Models 2
TT 42.4: Vortrag
Donnerstag, 26. März 2009, 14:45–15:00, HSZ 301
Effective low-energy theory for the kagomerized Kitaev model — •Michael Kamfor1, Julien Vidal2, Sébastien Dusuel3, and Kai Phillip Schmidt1 — 1Technische Universität Dortmund Lehrstuhl für Theoretische Physik I, Germany — 2Université Pierre et Marie Curie Paris 06, France — 3Lycée Saint-Louis, 75006 Paris, France
The Kitaev model on the honeycomb lattice is a two-dimensional quantum spin model containing abelian and non-abelian anyonic excitations [1]. The effective low-energy theory in the abelian gapped phase is the celebrated toric code relevant for topological quantum computation [2][3]. The usually studied limit of isolated dimers leads to an effective square lattice. The ground state is in the vortex-free sector. Excitations are low-energy abelian anyons and high-energy fermions. Here we study a different limit of isolated dimers giving rise to an effective Kagome lattice. We obtain the low-energy physics of the gapped phase in terms of abelian anyons on triangle and honeycomb plaquettes of the Kagome lattice using perturbative continuous unitary transformations [3][4]. The full phase diagram is calculated exactly by Majorana fermionization. Interestingly, the spectrum is always gapped except at the isotropic point. As a consequence, the non-abelian phase present in the usual honeycomb Kitaev model is reduced to a single point.
[1] A. Kitaev, Ann. Phys. (N.Y.) 303, 2 (2003).
[2] A. Kitaev, Ann. Phys. (N.Y.) 321, 2 (2006).
[3] K. P. Schmidt, S. Dusuel, and J. Vidal, Phys. Rev. Lett. 100, 057208 (2008).
[4] J. Vidal, K. P. Schmidt, and S. Dusuel, arXiv:0809.1553, accepted for Physical Review B.