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

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 four-body operator amplitudes, but reliable results require the use of a large Fock component in the exchange functional.