Application of Multi-Orbital DMFT to the Dynamic Hubbard Model

Fabian B. Kugler, Seung‐Sup B. Lee, Manuel Zingl +4 more

Christopher Polachic, F. Marsiglio

Qingguo Feng, Peter M Oppeneer

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.

Volodymyr Turkowski, Talat Shahnaz Rahman

Abstract We formulate a rigorous method for calculating a nonadiabatic (frequency-dependent) exchange-correlation (XC) kernel appropriate for accurate description of both equilibrium and nonequilibrium properties of strongly correlated systems within the time-dependent density functional theory (TDDFT) via the charge susceptibility, which is in turn obtained from dynamical mean field theory (DMFT) based on the effective multi-orbital Hubbard model. Application to the simple case of the one-orbital Hubbard model already shows the importance of the nonadiabatic kernel as it leads to significant modification of the excitation spectrum—shifting the (adiabatic) peak and disclosing another that is reminiscent of the solution from DMFT. The impact of dynamical effects, naturally included through the nonadiabaticity of the XC kernel, becomes even more transparent in our consideration of the nonequilibrium charge-density response of a multi-orbital perovskite, YTiO 3 , to a perturbation by a femtosecond (fs) laser pulse. These initial results indicate that electron–electron correlations and nonadiabatic features may significantly affect the spectrum and nonequilibrium properties of strongly correlated systems. We also propose an algorithm for extension of the approach to non-linear response. The transparency and computational efficiency of this non-adiabatic TDDFT+DMFT approach opens the door to examination of the spectra and response of multi-orbital systems with many nonequivalent atoms—bulk material, films and nanostructures.

Dominika Zgid, Emanuel Gull, Garnet Kin‐Lic Chan

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.

Volodymyr Turkowski