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arXiv:0801.0229 · Physical Review B

Exactly solvable Kitaev model in three dimensions

Saptarshi Mandal, Naveen Surendran

Published Jan 26, 2009• 200 citations
arXivHTMLPDF

Abstract

We introduce a spin-$\frac{1}{2}$ model in three dimensions which is a generalization of the well-known Kitaev model on a honeycomb lattice. Following Kitaev, we solve the model exactly by mapping it to a theory of noninteracting fermions in the background of a static ${\mathbb{Z}}_{2}$ gauge field. The phase diagram consists of a gapped phase and a gapless one, similar to the two-dimensional case. Interestingly, unlike in the two-dimensional model, in the gapless phase the gap vanishes on a contour in the $\mathbf{k}$ space. Furthermore, we show that the flux excitations of the gauge field, due to some local constraints, form looplike structures; such loops exist on a lattice formed by the plaquettes in the original lattice and is topologically equivalent to the pyrochlore lattice. Finally, we derive a low-energy effective Hamiltonian that can be used to study the properties of the excitations in the gapped phase.

DOI
10.1103/physrevb.79.024426

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