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Exactly solvable Kitaev model in three dimensions
We introduce a spin-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 non-interacting fermions
in the background of a static 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 k space. Furthermore, we show that the flux
excitations of the gauge field, due to some local constraints, form loop like
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.Comment: 9 pages, 7 figures; published version; a new section and more
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