Density functional theory along with Kohn-Sham formalism (DFT-KS) works well for weakly correlated electron systems such as alkali metals or systems involving atoms belonging to the first or second row of the periodic table. As a result, DFT-KS and its variants such as local spin density approximation (LSDA) or the generalized gradient approximation (GGA) encounter difficulties when applied to strongly correlated electron systems (SCES), such as transition metals, high-T_c superconductors (HTCS) and heavy fermion systems.

Problems of interacting electrons in 2d magnetic materials can be greatly simplified by reducing them to effective quantum spin models. The initial step is renormalizing the Hamiltonian into a lower energy subspace, miming the physics of the interested degrees of freedom. The Hubbard model is the so-called parent Hamiltonian in this field. A kinetic (hopping; t) term defines it on a lattice and a columb on-site interaction (U) for electrons. In the case of large Columb interaction, the double site occupation is not favored and should be projected out. This leads to the t-J model which has 3 degrees of freedom for each lattice site and consists of the kinetic and exchange terms.