Interpolative approach for solving the Anderson impurity model

Abstract

A rational representation for the self-energy is explored to interpolate the solution of the Anderson impurity model in general orbitally degenerate case. Several constrains such as the Friedel's sum rule, positions of the Hubbard bands as well as the value of quasiparticle residue are used to establish the equations for the coefficients of the interpolation. We employ two fast techniques, the slaveboson mean-field and the Hubbard I approximations to determine the functional dependence of the coefficients on doping, degeneracy and the strength of the interaction. The obtained spectral functions and self-energies are in good agreement with the results of numerically exact quantum Monte Carlo method.

Optical spectroscopy and the nature of the insulating state of rare-earth nickelates

“…The self-energies at LB and SB sites behave very differently. The LB self-energy exhibits a strongly singular behavior at small frequencies suggesting that a representation by a rational fraction 35 is adequate. In fact, we have found that the following two-pole ansatz is sufficient to represent the LB self-energy with high accuracy:…”

Many-Body Electronic Structure of Americium Metal

“…The key insight is that the above form of the self energy with a few poles captures [9,14] all the central features of a correlated system and is an excellent approximation to the Greens function of the system for the purposes of obtaining the total energy. This has an important implication for the calculation of the electronic structure of the strongly correlated material: once pole expansion of the self-energy is established, the spectral density functional theory reduces to solving a "Kohn Sham-like" system of equations in an augmented space.…”

Dynamical mean-field theory within the full-potential methods: Electronic structure ofCeIrIn5,CeCoIn5, andHaule1, Yee2, Kim3 2010Phys. Rev. B

“…There are three major issues that arise in DFT+DMFT implementations: i) quality of the basis set, ii) quality of the impurity solvers, and iii) choice of correlated orbitals onto which the full Green's function is projected. Modern DFT implementations largely resolve the first issue, recent development of new impurity solvers [21][22][23][25][26][27]29 have focused attention on the second, while the third is rarely discussed in the literature. Many DFT+DMFT proposals in the literature are based on downfolding to low energy model Hamiltonians 2, 19,20,28 , which requires an atomic set of orbitals and treats the kinetic operator on the level of an effective tight binding model.…”