Atomic Fermi gas in the trimerized Kagom\'e lattice at the filling 2/3
  We study low temperature properties of an atomic spinless interacting Fermi gas in the trimerized Kagom\'e lattice for the case of two fermions per trimer. The system is described by a quantum spin 1/2 model on the triangular lattice with couplings depending on bonds directions. Using exact diagonalizations we show that the system exhibits non-standard properties of a {\it quantum spin-liquid crystal}, combining a planar antiferromagnetic order with an exceptionally large number of low energy excitations. 
B. Damski, H.-U. Everts, A. Honecker, H. Fehrmann, L. Santos and M.   Lewenstein