Heavy localized + light itinerant electrons — charge ordering phases
The Falicov-Kimball model describes two species: heavy (f) electrons that are localized and form a classical binary field w_i ∈ {0,1}, and light (c) electrons that hop with amplitude t. The f-electrons' static configuration is determined by minimizing the free energy. At half-filling (n_f=0.5) and large U, a checkerboard charge-density wave forms below a critical temperature.