@article {1175, title = {Kitaev honeycomb and other exotic spin models with polar molecules}, journal = {Molecular Physics}, volume = {111}, year = {2013}, month = {2013/01/01}, pages = {1908 - 1916}, abstract = { 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. }, doi = {10.1080/00268976.2013.800604}, url = {http://arxiv.org/abs/1301.5636v1}, author = {Alexey V. Gorshkov and Kaden R. A. Hazzard and Ana Maria Rey} }