We show that ultracold polar molecules pinned in an optical lattice can be
used to access a variety of exotic spin models, including the Kitaev honeycomb
model. Treating each molecule as a rigid rotor, we use DC electric and
microwave fields to define superpositions of rotational levels as effective
spin degrees of freedom, while dipole-dipole interactions give rise to
interactions between the spins. In particular, we show that, with sufficient
microwave control, the interaction between two spins can be written as a sum of
five independently controllable Hamiltonian terms proportional to the five
rank-2 spherical harmonics Y_{2,q}(theta,phi), where (theta,phi) are the
spherical coordinates of the vector connecting the two molecules. To
demonstrate the potential of this approach beyond the simplest examples studied
in [S. R. Manmana et al., arXiv:1210.5518v2], we focus on the realization of
the Kitaev honeycomb model, which can support exotic non-Abelian anyonic
excitations. We also discuss the possibility of generating spin Hamiltonians
with arbitrary spin S, including those exhibiting SU(N=2S+1) symmetry.
