Topological phases in ultracold polar-molecule quantum magnets

We show how to use polar molecules in an optical lattice to engineer quantum
spin models with arbitrary spin S >= 1/2 and with interactions featuring a
direction-dependent spin anisotropy. This is achieved by encoding the effective
spin degrees of freedom in microwave-dressed rotational states of the molecules
and by coupling the spins through dipolar interactions. We demonstrate how one
of the experimentally most accessible anisotropies stabilizes symmetry
protected topological phases in spin ladders. Using the numerically exact
density matrix renormalization group method, we find that these interacting
phases -- previously studied only in the nearest-neighbor case -- survive in
the presence of long-range dipolar interactions. We also show how to use our
approach to realize the bilinear-biquadratic spin-1 and the Kitaev honeycomb
models. Experimental detection schemes and imperfections are discussed.