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    Exact results for the star lattice chiral spin liquid


    Kells, G. and Mehta, D. and Slingerland, Joost and Vala, Jiri (2010) Exact results for the star lattice chiral spin liquid. Physical Review B, 81 (104429). pp. 1-8. ISSN 1098-0121

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    Abstract

    We examine the star lattice Kitaev model whose ground state is a chiral spin liquid. We fermionize the model such that the fermionic vacua are toric-code states on an effective Kagome lattice. This implies that the Abelian phase of the system is inherited from the fermionic vacua and that time-reversal symmetry is spontaneously broken at the level of the vacuum. In terms of these fermions we derive the Bloch-matrix Hamiltonians for the vortex-free sector and its time-reversed counterpart and illuminate the relationships between the sectors. The phase diagram for the model is shown to be a sphere in the space of coupling parameters around the triangles of the lattices. The Abelian phase lies inside the sphere and the critical boundary between topologically distinct Abelian and non-Abelian phases lies on the surface. Outside the sphere the system is generically gapped except in the planes where the coupling parameters between the vertices on triangles are zero. These cases correspond to bipartite lattice structures and the dispersion relations are similar to that of the original Kitaev honeycomb model. In a further analysis we demonstrate the threefold non-Abelian ground-state degeneracy on a torus by explicit calculation.

    Item Type: Article
    Additional Information: The definitive version of this article is available at DOI: 10.1103/PhysRevB.81.104429
    Keywords: star lattice; chiral spin liquid; Kitaev model;
    Academic Unit: Faculty of Science and Engineering > Mathematical Physics
    Item ID: 4527
    Depositing User: Dr. Jiri Vala
    Date Deposited: 01 Oct 2013 14:36
    Journal or Publication Title: Physical Review B
    Publisher: American Physical Society
    Refereed: Yes
    URI:

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