Estimation of biquadratic and bicubic Heisenberg effective couplings from multiorbital Hubbard models

Abstract We studied a multi-orbital Hubbard model at half-filling for two and three orbitals per site on two-site cluster via full exact diagonalization, in wide range the onsite repulsion U , from weak to strong coupling, multiple ratios of Hund coupling J H . The hopping matrix elements among were also varied extensively. At intermediate large we mapped results into Heisenberg model. For site, mapping is S = 1 where by symmetry both nearest-neighbor ( i ⋅ j ) ( S i ⋅ j stretchy="false">) 2 are allowed, with respective couplings 2 case 3/2 ), {\mathbf{S}}_{j})}^{3}$?> 3 terms, 3 strength these constants models depend amplitudes underlying Our study provides first crude estimate establish bounds how / can be. show that those appear rather limited and, as qualitative guidance, conclude less than 0.4 0.2, establishing effective strongly correlated systems. Moreover, regime was found be most promising enhance