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Europhysics Letters (EPL)

Effect of nonlocal charge correlations on the Mott-Hubbard transition

Tran Minh-Tien

Published Sep 1, 1999• 3 citations
Publisher

Abstract

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.

DOI
10.1209/epl/i1999-00423-y

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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.
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 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.
In this paper, we investigate the impact of nonlocal correlations on charge fluctuations in the two-dimensional single-band Hubbard model close to the Mott metal-to-insulator transition, employing the ladder dynamical vertex approximation. At half filling and for interaction strengths and temperatures where the system is in the Mott insulating phase, charge fluctuations are strongly suppressed. Under these conditions, dynamical mean-field theory (DMFT) calculations predict a strong enhancement of the charge susceptibility at small (electron or hole) doping. However, these DMFT results include only the effects of purely local correlations despite the importance of nonlocal correlations in two-dimensional systems. We have, hence, carried out ladder dynamical vertex approximation $(\mathrm{lD}\mathrm{\ensuremath{\Gamma}}\mathrm{A})$ simulations which allow for the inclusion of such nonlocal correlation effects while retaining the local ones of DMFT. Our $\mathrm{lD}\mathrm{\ensuremath{\Gamma}}\mathrm{A}$ numerical data show that close to half filling the large uniform charge susceptibility of DMFT is strongly suppressed by nonlocal fluctuations but gradually increases with (electron) doping. At a certain doping value, charge fluctuations eventually become larger in $\mathrm{lD}\mathrm{\ensuremath{\Gamma}}\mathrm{A}$ with respect to DMFT, indicating that the absence of nonlocal correlations underestimates the mobility of the charge carriers in this parameter regime. This metallization effect is also reflected in an enhancement of the $\mathrm{lD}\mathrm{\ensuremath{\Gamma}}\mathrm{A}$ kinetic and potential energies and a corresponding reduction of the (absolute value of the) $\mathrm{lD}\mathrm{\ensuremath{\Gamma}}\mathrm{A}$ Matsubara self-energy with respect to DMFT.
We study the half-filled extended Hubbard model on a two-dimensional square lattice using cluster dynamical mean-field theory on clusters of size 8--20. We show that the model exhibits metallic, Mott-insulating, and charge-ordered phases, and determine the location of the charge-ordering phase-transition line and the properties of the phases as a function of temperature, local interaction, and nearest-neighbor interaction. We find strong nonlocal correlations outside the charge-ordered phase and a pronounced screening effect in the vicinity of the phase transition, where nonlocal interactions push the system towards metallic behavior. In contrast, correlations in the charge-ordered phase are mostly local to the unit cell. Finally, we demonstrate how strong nonlocal electron-electron interactions can increase electron mobility by turning a charge-ordered insulator into a metal. We analyze finite-size effects and the convergence of our data to the thermodynamic limit. Control of all sources of errors allows us to assess the regime of applicability of simpler approximation schemes for systems with nonlocal interactions.
The statistical dynamical mean field theory is used to study the metal-insulator transition in the two-dimensional Falicov-Kimball model with local disorder. Within the theory, the local density of states and its distributions are calculated. As a measure of the metal-insulator transition driven by correlation and disorder, the most probable value of the local density of states is determined. The most probable value of the local density of states is found to exhibit a discontinuity when the system crosses from extended states to localization. A phase diagram is also presented.
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.