Trifocal tensor

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 И. Хомский). The Hamiltonian used is:

$H=\frac{t^2}{U}\sum _{⟨i,j⟩}[4(\overrightarrow{S_i}\cdot \overrightarrow{S_j})({\tau }_i^{\alpha }-\frac{1}{2})({\tau }_j^{\alpha }-\frac{1}{2})+({\tau }_i^{\alpha }+\frac{1}{2})({\tau }_j^{\alpha }+\frac{1}{2})-1]$

References

• http://kotliar6.rutgers.edu/udo/prof/profd/papers/prb56_14243.pdf
• K. I. Kugel and D. I. Khomskii, Sov. Phys. Usp. 25, 231 (1982).

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