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The four-spin operators are suspected to have a significant amplitude and an impact on the collectiveproperties in spin ladders and magnetic two-dimensional lattices. They originate from cyclic circulation ofelectrons ~ring currents!. Starting from a simple Hubbard Hamiltonian one may establish their form from afourth order expansion of quasidegenerate perturbation theory. This form slightly deviates from the generallyassumed biquadratic expression. From a quantitative point of view, their amplitude can be assessed fromaccurate ab initio explicitly correlated wave functions and energies on embedded clusters. The present workshows that symmetry-broken density functional theory calculations may also provide estimates of the fourbodyoperator amplitudes, but reliable results require the use of a large Fock component in the exchangefunctiona

Origin and evaluation of the four-spin operators in magnetic lattices