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arXiv:cond-mat/9704028

Quasiparticle Many-Body Dynamics of Highly Correlated Electronic Systems

A. L. Kuzemsky

Published Apr 3, 1997• 3 citations
arXivHTMLPDF

Abstract

The self-consistent theory of the correlation effects in Highly Correlated Systems(HCS) is presented. The novel Irreducible Green's Functions(IGF) method is discused in detail for the Hubbard model and random Hubbard model. The interpolative solution for the quasiparticle spectrum, which is valid for both the atomic and band limit is obtained. The (IGF) method permits to calculate the quasiparticle spectra of many-particle systems with the complicated spectra and strong interaction in a very natural and compact way. The inelastic scattering corrections leads to the damping of the quasiparticles and are the main topic of the present consideration. The calculation of the damping has been done in a self-consistent way for both limits. For the random Hubbard model the weak coupling case has been considered and the self-energy operator has been calculated using the combination of the IGF method and Coherent Potential Approximation (CPA). The other applications of the method to s-f model, Anderson model, Heisenberg antiferromagnet, electron-phonon interaction models are discussed briefly.

DOI
10.48550/arxiv.cond-mat/9704028

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The self-consistent theory of the correlation effects in Highly Correlated Systems(HCS) is presented. The novel Irreducible Green's Functions(IGF) method is discused in detail for the Hubbard model and random Hubbard model. The interpolative solution for the quasiparticle spectrum, which is valid for both the atomic and band limit is obtained. The (IGF) method permits to calculate the quasiparticle spectra of many-particle systems with the complicated spectra and strong interaction in a very natural and compact way. The inelastic scattering corrections leads to the damping of the quasiparticles and are the main topic of the present consideration. The calculation of the damping has been done in a self-consistent way for both limits. For the random Hubbard model the weak coupling case has been considered and the self-energy operator has been calculated using the combination of the IGF method and Coherent Potential Approximation (CPA). The other applications of the method to s-f model, Anderson model, Heisenberg antiferromagnet, electron-phonon interaction models are discussed briefly.
A review of electronic dynamics of single-impurity and many-impurity Anderson models is contained in this report. Those models are used widely for many of the applications in diverse fields of interest, such as surface physics, theory of chemisorption and adsorbate reactions on metal surfaces, physics of intermediate valence systems, theory of heavy fermions, physics of quantum dots and other nanostructures. While standard treatments are generally based on perturbation methods, our approach is based on the non-perturbative technique for the thermodynamic Green functions. The method of the irreducible Green functions is used as the basic tool. This irreducible Green functions method allows one to describe the quasiparticle spectra with damping of the strongly correlated electron systems in a very general and natural way and to construct the relevant dynamical solution in a self-consistent way on the level of Dyson equation without decoupling the chain of the equations of motion for the Green functions. The subject matter includes the improved interpolating solution of the Anderson model. It was shown that an interpolating approximation, which simultaneously reproduces the weak-coupling limit up to second order in the interaction strength U and the strong-coupling limit up to second order in the hybridization V (and thus also fulfils the atomic limit) can be formulated self-consistently. This approach offers a new way for the systematic construction of approximate interpolation dynamical solutions of strongly correlated electron systems.
The paper addresses the many-body quasiparticle dynamics of the Anderson impurity model at finite temperatures in the framework of the equation-of-motion method. We find a new exact identity relating the one-particle and many-particle Green’s functions. Using this identity we present a consistent and general scheme for a construction of generalized mean fields (elastic scattering corrections) and self-energy (inelastic scattering) in terms of Dyson equation. A new approach for the complex expansion for the single-particle propagator in terms of Coulomb repulsion U and hybridization V is proposed. Using the exact identity, the essentially new many-body dynamical solution of SIAM has been derived. This approach offers a new way for the systematic construction of the approximative interpolating dynamical solutions of the strongly correlated electron systems.
A new approach to many-body quasiparticle dynamics of the Anderson impurity model at flnite temperatures is proposed in the framework of the equation-of-motion method.We flnd a new exact identity, which relates the one-particle and many-particle Green functions.Using this identity, it is shown that a new interpolating approximation for the one-particle Green function can be constructed.The approximation which simultaneously reproduces tle weak-coupling limit and the strong coupling limit can be formulated self-consistently.This approach offers a new method for a systematic construction of the approximate interpolating dynamical solutions of strongly correlated electron models.
A theory of the single-particle excitation spectrum is presented on the basis of the projection operator method combined with the many-body coherent-potential approximation (CPA). The theory describes the dynamics of the excitations by means of an energy-dependent Liouville operator accompanied by a coherent potential which is determined by the self-consistent CPA condition. It is shown that the present theory is essentially equivalent to the dynamical CPA and the dynamical mean-field theory. The Hubbard III approximation and the modified perturbation theory are rederived from the theory. A renormalized perturbation scheme for the Green function is developed on the basis of a general formula for the memory function. It interpolates between the weak- and strong-Coulomb interaction limits, and yields the metal-insulator transition for half-filled bands. Numerical calculations have been performed for the Gutzwiller-Hubbard model on a hypercubic lattice in infinite dimensions. The results show that the theory describes quantitatively the quasiparticle weight vs Coulomb interaction curve, yielding a reasonable critical Coulomb interaction for the metal-insulator transition. It produces the overall features of the excitation spectra and the momentum distributions for various Coulomb interaction strengths.
Strong electronic correlations are the root of many fascinating phenomena of condensed matter physics. However, they also make calculations notoriously difficult. This thesis is concerned with the development and improvement of computational methods for strongly correlated electron systems. After a brief recapitulation of the Green’s function formalism,which is the theoretical basis of most such methods, we discuss the analytical continuation from imaginary to real frequencies. Especially the maximum entropy method is explained in detail and an implementation there of is presented.The remainder of this thesis deals with methods to compute Green’s functions on thei maginary frequency axis. First, the Anderson impurity model (AIM) is considered. It can be solved numerically – a task for which several methods exist. We focus on continuous-time quantum Monte Carlo with worm sampling, through which various kinds of correlation functions can be calculated. On this basis we derive and implement symmetric improved estimators that allow for the computation of the self-energy and vertex functions where the level of stochastic noise is largely reduced with respect to conventional estimators.As a next step the dynamical mean-field theory (DMFT) is introduced as a method to capture local correlations in the Hubbard model (HM) by self-consistently mapping it onto the AIM. We study the convergence behavior of this iterative procedure and the improvement of convergence due to mixing. Then, we compare electron scattering rates from DMFT in the weak-coupling regime of the square-lattice HM to results from Boltzmann scattering theory.While local correlations account for many interesting phenomena, such as the Mott-Hubbard metal-insulator transition, they are not sufficient to correctly describe, e.g., the physics of phase transitions in two- or three-dimensional systems. It is thus the final step in this thesis to also include nonlocal correlations by means of the dynamical vertex approximation (DΓA). For this we develop a new self-consistency scheme, which is then applied to several systems: We study the square-lattice HM, where we compare to benchmark methods in the weak-coupling regime, but also present results for intermediate and strong coupling. Furthermore, a two-band model with doping and a three-band Wannier model for strontium vanadate are studied. As an application of our new self-consistent DΓA, we study the effects of geometrical frustration in the kagome lattice, where we also compare our results to determinant quantum Monte Carlo.
We study the quasiparticle spectrum of the Hubbard model by using a projection-operator formalism of the Green's function. In the weak-electron-correlation regime, we obtain the exact results up to second order in the intra-atomic interaction. For strong electron correlations, the quasiparticle spectrum consists of two bands. For each band, the quasiparticle energy is obtained exactly up to the first order in the transfer integral. We also propose a semiclassical approximation which gives the above-mentioned exact results in proper limits.