Multiplet effects in orbital and spin ordering phenomena: A hybridization-expansion quantum impurity solver study

We use an efficient general hybridization-expansion continuous-time quantum Monte Carlo impurity solver (Krylov approach) to study orbital and spin ordering phenomena in strongly correlated systems within the local-density approximation plus dynamical mean-field theory approach. This allows us to include often-neglected interaction terms, to study models with large basis sets, to consider crystals with low-symmetry distortions, and to reach the very low experimental temperatures. We use this solver to study ordering phenomena in a selection of exemplary low-symmetry transition-metal oxides. For the rare-earth manganites, we show that including spin-flip and pair-hopping terms does not affect the Kugel-Khomskii orbital-order melting transition. For LaMnO${}_3$, we find that the commonly used two-band model with classical $t_{2g}$ spin gives a good description of the $e_g$ electrons when compared with the full five-orbital Hubbard model. Surprisingly not only the occupied orbital but also the $e_g$ spectral matrix is well reproduced. For the $d^1$ perovskites CaVO${}_3$ and YTiO${}_3$ we show that spin-flip and pair-hopping terms only weakly affect orbital fluctuations. Moreover, for the Mott insulator YTiO${}_3$ we can study the ferromagnetic polarization to very low temperatures, finding a transition temperature in remarkably good agreement with experiments.