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Statut |
Confirmé |
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Série |
CONDMAT-ENS |
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Domaines |
cond-mat |
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Date |
Mardi 1 Juin 2010 |
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Heure |
10:45 |
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Institut |
LPS/ENS |
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Salle |
Con. IV |
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Nom de l'orateur |
Vala |
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Prenom de l'orateur |
Jiri |
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Addresse email de l'orateur |
jiri [dot] vala [at] nuim [dot] ie |
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Institution de l'orateur |
Department of Mathematical Physics, National University of Ireland, Ireland |
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Titre |
Exact results on Kitaev-like lattice models |
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Résumé |
Topological phases of matter have attracted considerable attention recently for both fundamental reasons and potential applications. They are formed in two-dimensional strongly correlated condensed matter systems and permit quasi-particle excitations with fractional statistics that have potential applications in topological quantum information processing.
The Kitaev honeycomb lattice model exhibits the Abelian and non-Abelian topological phases. These are effectively described by the doubled-Z2 and the Ising topological field theory respectively. We present a novel exact solution of the Kitaev spin model on the honeycomb lattice. We employ a Jordan-Wigner type fermionization and find that the Hamiltonian takes a BCS type form, allowing the system to be solved by Bogoliubov transformation. Our fermionization does not employ non-physical auxiliary degrees of freedom and the eigenstates we obtain are completely explicit in terms of the spin variables. The ground-state is obtained as a BCS condensate of fermion pairs over a vacuum state which corresponds to the toric code state with the same vorticity. We show in detail how to calculate all eigenstates and eigenvalues of the model on the torus. In particular, we find that the topological degeneracy on the torus descends directly from that of the toric code, which now supplies four vacua for the fermions, one for each choice of periodic vs. anti-periodic boundary conditions. The reduction of the degeneracy in the non-Abelian phase of the model is seen to be due to the vanishing of one of the corresponding candidate BCS ground-states in that phase. This occurs in particular in the fully periodic vortex-free sector. The true ground-state in this sector is exhibited and shown to be gapped away from the three partially anti-periodic ground-states whenever the non-Abelian topological phase is gapped. The solution of the related star lattice chiral spin liquid, along with the recent results on the edge states and Berry phase calculations associated with anyonic braiding will be also briefly presented.
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Numéro de preprint arXiv |
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