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arXiv:1108.2921 · Journal of Physics Condensed Matter

An advanced multi-orbital impurity solver for dynamical mean field theory based on the equation of motion approach

Qingguo Feng, P. M. Oppeneer

Published Jan 17, 2012• 7 citations
arXivHTMLPDF

Abstract

We propose an improved fast multi-orbital impurity solver for the dynamical mean field theory based on equations of motion (EOM) for Green's functions and a decoupling scheme. In this scheme the inter-orbital Coulomb interactions are treated fully self-consistently, and involve the inter-orbital fluctuations. As an example of the use of the derived multi-orbital impurity solver, the two-orbital Hubbard model is studied for various cases. Comparisons are made between numerical results obtained with our EOM scheme and those obtained with quantum Monte Carlo and numerical renormalization group methods. The comparison shows a good agreement, but also reveals a dissimilarity of the behaviors of the densities of states which is caused by inter-site inter-orbital hopping effects and on-site inter-orbital fluctuation effects, thus corroborating the assertion of the value of the EOM method for the study of multi-orbital strongly correlated systems.

DOI
10.1088/0953-8984/24/5/055603

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We propose an improved fast multi-orbital impurity solver for the dynamical mean field theory based on equations of motion (EOM) for Green's functions and a decoupling scheme. In this scheme the inter-orbital Coulomb interactions are treated fully self-consistently, and involve the inter-orbital fluctuations. As an example of the use of the derived multi-orbital impurity solver, the two-orbital Hubbard model is studied for various cases. Comparisons are made between numerical results obtained with our EOM scheme and those obtained with quantum Monte Carlo and numerical renormalization group methods. The comparison shows a good agreement, but also reveals a dissimilarity of the behaviors of the densities of states which is caused by inter-site inter-orbital hopping effects and on-site inter-orbital fluctuation effects, thus corroborating the assertion of the value of the EOM method for the study of multi-orbital strongly correlated systems.
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.
We implement an efficient numerical method to calculate response functions of complex impurities based on the Density Matrix Renormalization Group (DMRG) and use it as the impurity-solver of the Dynamical Mean Field Theory (DMFT). This method uses the correction vector to obtain precise Green's functions on the real frequency axis at zero temperature. By using a self-consistent bath configuration with very low entanglement, we take full advantage of the DMRG to calculate dynamical response functions paving the way to treat large effective impurities such as those corresponding to multi-orbital interacting models and multi-site or multi-momenta clusters. This method leads to reliable calculations of non-local self energies at arbitrary dopings and interactions and at any energy scale.
We implement an efficient numerical method to calculate response functions of complex impurities based on the Density Matrix Renormalization Group (DMRG) and use it as the impurity-solver of the Dynamical Mean Field Theory (DMFT). This method uses the correction vector to obtain precise Green's functions on the real frequency axis at zero temperature. By using a self-consistent bath configuration with very low entanglement, we take full advantage of the DMRG to calculate dynamical response functions paving the way to treat large effective impurities such as those corresponding to multi-orbital interacting models and multi-site or multi-momenta clusters. This method leads to reliable calculations of non-local self energies at arbitrary dopings and interactions and at any energy scale.
The natural orbitals renormalization group (NORG) has previously been proposed as an efficient numerical method for solving zero-temperature properties of multisite and multiorbital quantum impurity systems. Here, we implement the NORG as an impurity solver for dynamical mean-field theory (DMFT). In comparison with the exact diagonalization method, the NORG method can treat much more bath sites in an impurity model to which the DMFT maps a lattice model and can find accurate zero-temperature Matsubara and low-frequency retarded Green's functions. We demonstrate the effectiveness of this method on a two-orbital Hubbard model on the Bethe lattice and find successfully the orbital selective Mott transition with a Kondo resonance peak in the wide band and two holon-doublon bound state excitation peaks in the narrow band.
In this paper a fast impurity solver is proposed for dynamical mean-field theory (DMFT) based on a decoupling of the equations of motion for the impurity Green's function. The resulting integral equations are solved efficiently with a method based on genetic algorithms. The Hubbard and periodic Anderson models are studied with this impurity solver. The method describes the Mott metal-insulator transition and works for a large range of parameters at finite temperature on the real frequency axis. This makes it useful for the exploration of real materials in the framework of local-density approximation+DMFT\text{approximation}+\text{DMFT}approximation+DMFT.
The solution of an auxiliary quantum impurity system is the computationally expensive step in dynamical mean field theory simulations of lattice models and materials. In this review, we discuss Monte Carlo based impurity solvers, which are suitable for a wide range of applications. In particular, we present an efficient implementation of the hybridization expansion approach, which enables the simulation of multiorbital impurity problems with off-diagonal and complex hybridizations, and dynamically screened (retarded) density-density interactions. As a complementary approach, we discuss an impurity solver based on the determinant Monte Carlo method, which scales favorably with inverse temperature and hence provides access to the very low temperature regime. The usefulness of these state-of-the-art impurity solvers is demonstrated with applications to the downfolding problem, i.e., the systematic derivation of dynamically screened interactions for low-energy effective models, and to pyrochlore iridates, where the spin-orbit coupling leads to complex hybridization functions in a multi-orbital system. As a benchmark for cluster extensions of dynamical mean field theory, we also present results from lattice Monte Carlo simulations for the momentum dependence of the pseudo-gap in the half-filled two-dimensional Hubbard model.