Kugel–Khomskii coupling

Kugel–Khomskii coupling describes a coupling between the spin and orbital degrees of freedom in a solid; it is named after the Russian physicists Kliment I. Kugel (Климент Ильич Кугель) and Daniel I. Khomskii (Daniil I. Khomskii, Даниил Ильич Хомский). The Hamiltonian used is:

H = t 2 U ∑ ⟨ i , j ⟩ [ 4 ( S i → ⋅ S j → ) ( τ i α − 1 2 ) ( τ j α − 1 2 ) + ( τ i α + 1 2 ) ( τ j α + 1 2 ) − 1 ]