Efficient real-frequency solver for dynamical mean-field theory (original) (raw)
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Frontiers in Physics, 2018
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 impuritysolver 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.
Chinese Physics B, 2010
An impurity solver for the dynamical mean field (DMFT) study of the Mott insulators is proposed, which is based on the second order perturbation of the hybridization function. After carefully benchmarking it with Quantum Monte Carlo results on the anti-ferromagnetic phase of the Hubbard model, we conclude that this impurity solver can capture the main physical features in the strong coupling regime and can be a very useful tool for the LDA+DMFT studies of the Mott insulators with long range order.
Fast multi-orbital equation of motion impurity solver for dynamical mean field theory
Journal of Physics: Condensed Matter, 2011
We propose a fast multi-orbital impurity solver for the dynamical mean field theory (DMFT). Our DMFT solver is based on the equations of motion (EOM) for local Green's functions and constructed by generalizing from the single-orbital case to the multi-orbital case with 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 QMC method is made for the two-orbital Hubbard model and a good agreement is obtained. The developed method hence holds promise as a fast DMFT impurity solver in studies of strongly correlated systems.
Dynamical Mean Field Theory with the Density Matrix Renormalization Group
Physical Review Letters, 2004
A new numerical method for the solution of the Dynamical Mean Field Theory's self-consistent equations is introduced. The method uses the Density Matrix Renormalization Group technique to solve the associated impurity problem. The new algorithm makes no a priori approximations and is only limited by the number of sites that can be considered. We obtain accurate estimates of the critical values of the metal-insulator transitions and provide evidence of substructure in the Hubbard bands of the correlated metal. With this algorithm, more complex models having a larger number of degrees of freedom can be considered and finite-size effects can be minimized. PACS numbers: 71.10.Fd, 71.27.+a, 71.30.+h Great theoretical progress in our understanding of the physics of strongly correlated electron systems has been possible since the introduction of the Dynamical Mean Field Theory (DMFT) just over ten years now . This approach is based on the natural extension of the familiar classical mean-field theory of statistical mechanics to the treatment of models of strongly interacting electrons on a lattice. The DMFT solution of the model is exact in the limit of large lattice dimensionality or large connectivity [2, 3]. Since its introduction, DMFT has been widely adopted and was used for the investigation of a large variety of model Hamiltonians relevant for problems as diverse as colossal magneto-resistance, heavy fermions, metal-insulator transitions, etc. . A great deal of interest is currently centered around the ongoing efforts to incorporate DMFT as the local correlation physics "engine" for first-principle calculations of realistic compounds . At the heart of the DMFT method is the solution of an associated quantum impurity model where the environment of the impurity has to be determined self-consistently. Therefore the ability to obtain reliable DMFT solutions of lattice model Hamiltonians relies directly on the ability to solve quantum impurity models. Since solutions of general impurity models are usually not analytically tractable, one has to resort to numerical algorithms or approximate methods. Among the a priori exact numerical algorithms available we count the Hirsch-Fye Quantum Monte Carlo [6] method and Wilson's Numerical Renormalization Group (NRG) . The former is a finite-temperature method that is formulated in imaginary time and has been applied to a large variety of impurity models including the multi-orbital case that corresponds to correlated multi-band lattice Hamiltoni- * Present address: DFMC, Unicamp, Campinas, São Paulo, Brasil.
Augmented hybrid exact-diagonalization solver for dynamical mean field theory
2012
We present a new methodology to solve the Anderson impurity model, in the context of dynamical mean-field theory, based on the exact diagonalization method. We propose a strategy to effectively refine the exact diagonalization solver by combining a finite-temperature Lanczos algorithm with an adapted version of the cluster perturbation theory. We show that the augmented diagonalization yields an improved accuracy in the description of the spectral function of the single-band Hubbard model and is a reliable approach for a full d-orbital manifold calculation.
State-of-the-art techniques for calculating spectral functions in models for correlated materials
EPL (Europhysics Letters), 2015
The dynamical mean field theory (DMFT) has become a standard technique for the study of strongly correlated models and materials overcoming some of the limitations of density functional approaches based on local approximations. An important step in this method involves the calculation of response functions of a multiorbital impurity problem which is related to the original model. Recently there has been considerable progress in the development of techniques based on the density matrix renormalization group (DMRG) and related matrix product states (MPS) implying a substantial improvement to previous methods. In this article we review some of the standard algorithms and compare them to the newly developed techniques, showing examples for the particular case of the half-filled two-band Hubbard model.
Spectral Density Functional Approach to Electronic Correlations and Magnetism in Crystals
Electron Correlations and Materials Properties 2, 2002
A novel approach to electronic correlations and magnetism of crystals based on realistic electronic structure calculations is reviewed. In its simplest form it is a combination of the "local density approximation" (LDA) and the dynamical mean field theory (DMFT) approaches. Using numerically exact QMC solution to the effective DMFT multi-orbital quantum-impurity problem, a successful description of electronic structure and finite temperature magnetism of transition metals has been achieved. We discuss a simplified perturbation LDA+DMFT scheme which combines the T-matrix and fluctuation-exchange approximation (TM-FLEX). We end with a discussion of cluster generalization of the non-local DMFT scheme and its applications to the magnetism and superconductivity of high-Tc superconductors.
Journal of Chemical Theory and Computation, 2013
We propose an approach to the electronic structure problem based on noninteracting electron pairs that has similar computational cost to conventional methods based on noninteracting electrons. In stark contrast to other approaches, the wave function is an antisymmetric product of nonorthogonal geminals, but the geminals are structured so the projected Schrodinger equation can be solved very efficiently. We focus on an approach where, in each geminal, only one of the orbitals in a reference Slater determinant is occupied. The resulting method gives good results for atoms and small molecules. It also performs well for a prototypical example of strongly correlated electronic systems, the hydrogen atom chain.