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arXiv:cond-mat/0406472 · Physical Review B

Decoupling method for dynamical mean-field theory calculations

Harald O. Jeschke, Gabriel Kotliar

Published Feb 3, 2005• 24 citations
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Abstract

In this paper we explore the use of an equation of motion decoupling method as an impurity solver to be used in conjunction with the dynamical mean field self-consistency condition for the solution of lattice models. We benchmark the impurity solver against exact diagonalization, and apply the method to study the infinite $U$ Hubbard model, the periodic Anderson model and the $pd$ model. This simple and numerically efficient approach yields the spectra expected for strongly correlated materials, with a quasiparticle peak and a Hubbard band. It works in a large range of parameters, and therefore can be used for the exploration of real materials using the local density approximation and dynamical mean field theory.

DOI
10.1103/physrevb.71.085103

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In this paper we explore the use of an equation of motion decoupling method as an impurity solver to be used in conjunction with the dynamical mean field self-consistency condition for the solution of lattice models. We benchmark the impurity solver against exact diagonalization, and apply the method to study the infinite UUU Hubbard model, the periodic Anderson model and the pdpdpd model. This simple and numerically efficient approach yields the spectra expected for strongly correlated materials, with a quasiparticle peak and a Hubbard band. It works in a large range of parameters, and therefore can be used for the exploration of real materials using the local density approximation and dynamical mean field theory.
We propose using an equation-of-motion approach as an impurity solver for dynamical mean field theory. As an illustration of this technique, we consider a finite-U Hubbard model defined on the Bethe lattice with infinite connectivity at arbitrary filling. Depending on the filling, the spectra that is obtained exhibits a quasiparticle peak, and lower and upper Hubbard bands as typical features of strongly correlated materials. The results are also compared and in good agreement with exact diagonalization. We also find a different picture of the spectral weight transfer than the iterative perturbation theory.
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.
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 here present how a self-consistent solution of the dynamical mean field theory equations can be obtained using exact diagonalization of an Anderson impurity model with accuracies comparable to those found using renormalization group or quantum Monte Carlo methods. We show how one can solve a correlated quantum impurity coupled to several hundred uncorrelated bath sites, using a restricted active basis set. The number of bath sites determines the resolution of the obtained spectral function, which consists of peaks roughly spaced by the band width divided by the number of bath sites. The self-consistency cycles are fully performed on the real frequency axis and expressed as numerical stable matrix operations. The same impurity solver has been used on Ligand Field and finite size cluster calculations and is capable of treating involved Hamiltonians including the full rotational invariant Coulomb interaction, spin-orbit coupling and low symmetry crystal-fields. The proposed method allows for the calculation of a variety of correlation functions at little extra cost.
An investigation is presented of the utility of semiclassical approximations for solving the quantum-impurity problems arising in the dynamical-mean-field approach to correlated-electron models. The method is based on performing an exact numerical integral over the zero-Matsubara-frequency component of the spin part of a continuous Hubbard-Stratonovich field, along with a spin-field-dependent steepest descent treatment of the charge part. We test this method by applying it to one- or two-site approximations to the single-band Hubbard model with different band structures, and comparing the results to quantum Monte Carlo and simplified exact diagonalization calculations. The resulting electron self-energies, densities of states, and magnetic transition temperatures show reasonable agreement with the quantum Monte Carlo simulation over wide parameter ranges, suggesting that the semiclassical method is useful for obtaining a reasonable picture of the physics in situations where other techniques are too expensive.
We present an efficient exact diagonalization scheme for the extended dynamical mean-field theory and apply it to the extended Hubbard model on the square lattice with nonlocal charge-charge interactions. Our solver reproduces the phase diagram of this approximation with good accuracy. Details on the numerical treatment of the large Hilbert space of the auxiliary Holstein-Anderson impurity problem are provided. Benchmarks with a numerically exact strong-coupling continuous-time quantum Monte Carlo solver show better convergence behavior of the exact diagonalization in the deep insulator. Special attention is given to possible effects due to the discretization of the bosonic bath. We discuss the quality of real axis spectra and address the question of screening in the Mott insulator within extended dynamical mean-field theory.