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

TL;DR

This paper introduces an advanced quantum Monte Carlo impurity solver that enables realistic simulations of orbital and spin ordering in strongly correlated materials, capturing complex interactions and low-temperature phenomena.

Contribution

The authors develop a hybridization-expansion quantum impurity solver that includes interactions often neglected, allowing for more accurate modeling of orbital and spin ordering in complex materials.

Findings

Spin-flip and pair-hopping terms do not affect certain orbital transitions.

The solver accurately predicts the ferromagnetic transition temperature of YTiO3.

The classical spin approximation closely matches full orbital models in manganites.

Abstract

Orbital and spin ordering phenomena in strongly correlated systems are commonly studied using the local-density approximation + dynamical mean-field theory approach. Typically, however, such simulations are restricted to simplified models (density-density Coulomb interactions, high symmetry couplings and few-band models). In this work we implement an efficient general hybridization-expansion continuous-time quantum Monte Carlo impurity solver (Krylov approach) which allows us to investigate orbital and spin ordering in a more realistic setting, including interactions that are often neglected (e.g., spin-flip and pair-hopping terms), enlarged basis sets (full d versus eg), low-symmetry distortions, and reaching the very low-temperature (experimental) regime. We use this solver to study ordering phenomena in a selection of exemplary low-symmetry transition-metal oxides: LaMnO3 and rare-earth manganites as well as the perovskites CaVO3 and YTiO3. We show that spin-flip and pair hopping terms do not affect the Kugel-Khomskii orbital-order melting transition in rare-earth manganites, or the suppression of orbital fluctuations driven by crystal field and Coulomb repulsion. For the Mott insulator YTiO3 we find a ferromagnetic transition temperature 50 K, in remarkably good agreement with experiments. For LaMnO3 we show that the classical t2g-spin approximation, commonly adopted for studying manganites, yields indeed an occupied eg orbital in very good agreement with that obtained for the full d 5-orbital Hubbard model, while the spin-spin e_g-t_{2g} correlation function calculated from the full d model is 0.74, very close to the value expected for aligned eg and t2g spins; the eg spectral function matrix is also well reproduced. Finally, we show that the t2g screening reduces the eg-eg Coulomb repulsion by about 10%