Simplex solids in SU(N) Heisenberg models on the kagome and checkerboard   lattices
  We present a numerical study of the SU(N) Heisenberg model with the fundamental representation at each site for the kagome lattice (for N=3) and the checkerboard lattice (for N=4), which are the line graphs of the honeycomb and square lattices and thus belong to the class of bisimplex lattices. Using infinite projected entangled-pair states (iPEPS) and exact diagonalizations, we show that in both cases the ground state is a simplex solid state with a two-fold ground state degeneracy, in which the N spins belonging to a simplex (i.e. a complete graph) form a singlet. Theses states can be seen as generalizations of valence bond solid states known to be stabilized in certain SU(2) spin models. 
Philippe Corboz, Karlo Penc, Frederic Mila, Andreas M. Laeuchli
cond-mat.str-el cond-mat.quant-gas