These articles explore quantum simulation of quantum magnetism using ultracold atoms trapped in a lattice. Note that this is only a small selection of what currently appears in the literature.
Counterflow Superfluidity of Two-Species Ultracold Atoms in a Commensurate Optical Lattice
A. B. Kuklov and B. V. Svistunov
Phys. Rev. Lett. 90 , 100401 (2003)
Implementation of Spin Hamiltonians in Optical Lattices
J. J. Garcia-Ripoll , M. A. Martin-Delgado , J. I. Cirac
Phys. Rev. Lett. 93 , 250405 (2004)
* Controlling Spin Exchange Interactions of Ultracold Atoms in Optical Lattices
L.-M. Duan , E. Demler , and M. D. Lukin
Phys. Rev. Lett. 91 , 090402 (2003)
* Spin dynamics for bosons in an optical lattice
Garcia-Ripoll and Cirac,2003 New J. Phys. 5 76
Spin-dependent Hubbard model and a quantum phase transition in cold atoms
W. Vincent Liu , Frank Wilczek , and Peter Zoller
Phys. Rev. A 70 , 033603 (2004)
* Simulation of quantum dynamics with quantum optical systems
E. Jané , G. Vidal , W. Dür , P. Zoller , J.I. Cirac
quant-ph/0207011
* Spin-Spin Interaction and Spin Squeezing in an Optical Lattice
Anders Sørensen and Klaus Mølmer
Phys. Rev. Lett. 83, 2274 (1999)
*I'd recommend reading these articles first.