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Physical review. B, Condensed matter

Nonlocal dynamical correlations in the Falicov-Kimball model

Tran Minh-Tien

Published Dec 15, 1998• 4 citations
Publisher

Abstract

An extension of the dynamical mean-field approximation (DMFA) that allows for inclusion of nonlocal correlations is presented. This method is based on the projection technique and the DMFA, in which both local and nonlocal contributions to the dynamics of systems are evaluated exactly within a relevant subspace of Liouville space, while the remaining subspace is kept by local contributions. We examine the method by studying the spinless Falicov-Kimball model. It is found that the sum rules are preserved, the spectral function is positive definite, and nonlocal features of the spectral function appear, especially near the Fermi surface.

DOI
10.1103/physrevb.58.r15965

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We study the effects of correlated hopping in the two-dimensional (2D) Falicov-Kimball model by means of an extension of the dynamical mean-field approximation (DMFA). The extension is based on the projection technique and the DMFA, in which nonlocal correlations are taken into account through static quantities of a relevant subspace. The effect of the correlated hopping is to introduce nonlocal self-energy components which remain even at D → ∞ . We show that the sum rules of the spectral function and its moments are preserved. The spectral function obtained reveals significant nonlocal contributions which are absent in the DMFA.
We introduce an extension of the dynamical mean-field approximation (DMFA) that retains the causal properties and generality of the DMFA, but allows for systematic inclusion of nonlocal corrections. Our technique maps the problem to a self-consistently embedded cluster. The DMFA (exact result) is recovered as the cluster size goes to 1 (infinity). As a demonstration, we study the Falicov-Kimball model using a variety of cluster sizes. We show that the sum rules are preserved, the spectra are positive definite, and the nonlocal correlations suppress the charge-density wave transition temperature.
We study the two-dimensional Hubbard model by means of an extension of the dynamical mean-field approximation (DMFA). The extension is based on the projection technique and the DMFA, in which nonlocal contributions to the dynamics of the system are taken into account through static short-ranged correlations, while dynamical local contributions are kept by the local self-energy. The short-ranged correlations and the local self-energy are determined by mapping the lattice problem onto a self-consistently embedded cluster. We solve the cluster problem by using a noncrossing approximation. The spectral function obtained satisfies the sum rules of its first four moments. The spectra display pronounced nonlocal features including a pseudogap near the Fermi surface due to a competition between the Kondo-singlet formation and short-range spin correlations.
We propose a new, controlled approximation scheme that explicitly includes the effects of non-local correlations on the D = solution. In contrast to the usual D = case, the self-energy is self-consistently coupled to two-particle correlation functions. The formalism is general, and is applied to the two-dimensional Falicov-Kimball model. Our approach possesses all the strengths of the large- D solution, and allows one to undertake a systematic study of the effects of inclusion of k -dependent effects on the D = picture. Results for the density of states ( ), and the single-particle spectral density for the 2D Falicov-Kimball model always yield positive definite ( ), and the spectral function shows striking new features inaccessible for D = . Our results are in good agreement with the exact results known from the 2D Falicov-Kimball model.
The Mott-Hubbard transition is studied by examining the metal-insulator transition (MIT) in the homogeneous phase of the two-dimensional spinless Falicov-Kimball model. We use an extension of dynamical mean-field approximation, which allows inclusion of nonlocal correlations. The extension is based on the projection technique and the dynamical mean-field approximation, in which nonlocal contributions to the dynamics of systems are taken into account through static quantities, while the dynamical local contributions are kept by the memory function. We investigate critical behaviours of various dynamic and thermodynamic quantities near the MIT and estimate their critical exponents. The critical exponents obtained support a hyperscaling hypothesis and show a significant influence of nonlocal charge correlations on the transition.