Exact stripe, checkerboard, and droplet ground states in two dimensions
  Exact static nondegenerate stripe and checkerboard ground states are obtained in a two-dimensional generalized periodic Anderson model, for a broad concentration range below quarter filling. The random droplet states, also present in the degenerate ground state, are eliminated by extending the Hamiltonian with terms of different physical origin such as dimerization, periodic charge displacements, density waves, or distorsion lines. 
Zsolt Gulacsi and Miklos Gulacsi