Orbital magnetization is known empirically to play an important role in several magnetic phenomena, such as permanent magnetism and ferromagnetic superconductivity. Within the recently developed ``modern theory of orbital magnetization,'' theoretical insight has been gained into the nature of this often neglected contribution to magnetism but is based on an underlying mean-field approximation. From this theory, a few treatments have emerged which also take into account correlations beyond the mean-field approximation. Here, we apply the scheme developed in a previous work [F. Aryasetiawan et al., Phys. Rev. B 93, 161104(R) (2016)] to the spin-
21 Haldane-Hubbard model to investigate the effect of charge fluctuations on the orbital magnetization within the
GW approximation. Qualitatively, we are led to distinguish between two quite different situations: (i) When the lattice potential is larger than the nearest-neighbor hopping, the correlations are found to boost the orbital magnetization. (ii) If the nearest-neighbor hopping is instead larger than the lattice potential, the correlations reduce the magnetization. The boost and reduction are identified to stem from interband and intraband correlations, respectively, and the relative importance of the two varies with the strength of the lattice potential. We finally study graphene with parameters obtained from first principles.
The development of polynomial cost solvers for correlated quantum impurity models, with controllable errors, is a central challenge in quantum many-body physics, where these models find applications ranging from nanoscience to the dynamical mean-field theory (DMFT). Here, we describe how configuration interaction (CI) approximations to exact diagonalization (ED) may be used as solvers in DMFT. CI approximations retain the main advantages of ED, such as the ability to treat general interactions and off-diagonal hybridizations and to obtain real spectral information, but are of polynomial cost. Furthermore, their errors can be controlled by monitoring the convergence of physical quantities as a function of the CI hierarchy. Using benchmark DMFT applications, such as single-site DMFT of the one-dimensional Hubbard model and $2\ifmmode\times\else\texttimes\fi{}2$ cluster DMFT of the two-dimensional Hubbard model, we show that CI approximations allow us to obtain near-exact ED results for a tiny fraction of the cost. This is true over the entire range of interaction strengths including ``difficult'' regimes, such as in the pseudogap phase of the two-dimensional Hubbard model. We use the ability of CI approximations to treat large numbers of orbitals to demonstrate convergence of the bath representation in the $2\ifmmode\times\else\texttimes\fi{}2$ cluster DMFT using a 24-bath orbital representation. CI approximations thus form a promising route to extend ED to problems that are currently difficult to study using other solvers such as continuous-time quantum Monte Carlo, including impurity models with large numbers of orbitals and general interactions.
We propose a fast multi-orbital impurity solver for dynamical mean field theory (DMFT). Our DMFT solver is based on the equations of motion (EOMs) for local Green's functions and is constructed by generalizing from the single-orbital case to the multi-orbital case with the inclusion of the inter-orbital hybridizations and applying a mean field approximation to the inter-orbital Coulomb interactions. The two-orbital Hubbard model is studied using this impurity solver within a large range of parameters. The Mott metal-insulator transition and the quasiparticle peak are well described. A comparison of the EOM method with the quantum Monte Carlo method is made for the two-orbital Hubbard model and good agreement is obtained. The developed method hence holds promise as a fast DMFT impurity solver in studies of strongly correlated systems.