Quantum simulators realize microscopic quantum many body models on so-called optical lattices. Recently, it was shown that ultracold polar molecules can be used to emulate a generalized version of the t-J model, as well as XXZ models with anisotropic interactions in the spatial directions, e.g., as in compass models. Here, I discuss the behavior intwo simple situations: first I consider the phase diagram of the t-J_\perp chain, in which the usual Heisenberg exchange is replaced by a XX term, hence explicitly removing the SU(2) symmetry of the system. In 1D, this leads to an enhanced superconducting phase. In the second part I consider a S=1/2 2-leg ladder with XXZ interactions on the rungs and Heisenberg interactions along the legs. For nearest-neighbor couplings, symmetry protected topological phases are realized. I discuss to which extend these survive in the presence of long-range interactions as realized by the dipolar interactions between the molecules.

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