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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.