Exactly solvable Kitaev model in three dimensions

Details Exactly solvable Kitaev model in three dimensions Exactly solvable Kitaev model in three dimensions

2007-12-31

arxiv.org/abs/0801.0229v2

Phys. Rev. B 79, 024426 (2009)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

9 pages, 7 figures; published version; a new section and more references added

Scientific paper

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.

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