  We demonstrate that in a triangular configuration of an optical lattice of
two atomic species a variety of novel spin-1/2 Hamiltonians can be generated.
They include effective three-spin interactions resulting from the possibility
of atoms tunneling along two different paths. This motivates the study of
ground state properties of various three-spin Hamiltonians in terms of their
two-point and n-point correlations as well as the localizable entanglement. We
present a Hamiltonian with a finite energy gap above its unique ground state
for which the localizable entanglement length diverges for a wide interval of
applied external fields, while at the same time the classical correlation
length remains finite.
