Effective multi-body SU($N$)-symmetric interactions of ultracold fermionic atoms on a 3-D lattice.

Rapid advancements in the experimental capabilities with ultracold alkaline-earth-like atoms (AEAs) bring to a surprisingly near term the prospect of performing quantum simulations of spin models and lattice field theories exhibiting SU(N symmetry. Motivated in particular by recent experiments preparing high density samples of strongly interacting {}^{87}r atoms in a three-dimensional optical lattice, we develop a low-energy effective...