## Effective single-band models for strongly interacting fermions in an optical lattice

To test effective Hamiltonians for strongly interacting fermions in an optical lattice, we numerically find the energy spectrum for two fermions interacting across a Feshbach resonance in a double-well potential. From the spectrum, we determine the range of detunings for which the system can be described by an effective lattice model, and how the model parameters are related to the experimental parameters. We find that for a range of strong interactions the system is well described by an effective t-J model, and the effective superexchange term, J, can be smoothly tuned through zero on either side of unitarity. Right atmore »