Exactly solvable model for isospin S=3/2 fermionic atoms on an optical   lattice
  We propose an exact solution of a model describing a low energy behavior of cold isospin S=3/2 fermionic atoms on a one-dimensional optical lattice. Depending on the band filling the effective field theory has a form of a deformed Gross-Neveu model with either $O(7)\times \mathbb{Z}_2$ (half filling) or $U(1)\times O(5)\times \mathbb{Z}_2$ symmetry. 
D. Controzzi and A. M. Tsvelik