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Physical review. B, Condensed matter

Effect of strong correlations and static diagonal disorder in the d=∞ Hubbard model

M. S. Laad, L. Craco, E. Müller‐Hartmann

Published Oct 18, 2001• 47 citations
Publisher

Abstract

We investigate the effects of static, diagonal disorder in the $d=\ensuremath{\infty}$ Hubbard model by treating the dynamical effects of local Hubbard correlations and disorder on an equal footing. This is achieved by a proper combination of the iterated perturbation theory and the coherent-potential approximation. Within the paramagnetic phase, we find that the renormalized Fermi-liquid metal phase of the pure Hubbard model is stable against disorder for small disorder strengths. With increasing disorder, strong resonant scattering effects destroy low-energy Fermi-liquid coherence, leading to an incoherent metallic state off half-filling. Finally, for large enough disorder, a continuous transition to the disordered insulating phase occurs. The nature of the incoherent metallic phase, as well as the effects of the low-energy coherence (incoherence) on optical conductivity and electronic Raman spectra, are considered in detail.

DOI
10.1103/physrevb.64.195114

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We investigate the effects of static, diagonal disorder in the d=\ensuremath∞d=\ensuremath{\infty}d=\ensuremath∞ Hubbard model by treating the dynamical effects of local Hubbard correlations and disorder on an equal footing. This is achieved by a proper combination of the iterated perturbation theory and the coherent-potential approximation. Within the paramagnetic phase, we find that the renormalized Fermi-liquid metal phase of the pure Hubbard model is stable against disorder for small disorder strengths. With increasing disorder, strong resonant scattering effects destroy low-energy Fermi-liquid coherence, leading to an incoherent metallic state off half-filling. Finally, for large enough disorder, a continuous transition to the disordered insulating phase occurs. The nature of the incoherent metallic phase, as well as the effects of the low-energy coherence (incoherence) on optical conductivity and electronic Raman spectra, are considered in detail.
Disordered Hubbard model in d=∞d=\inftyd=∞
We investigate the effects of static, diagonal disorder in the d=∞d=\inftyd=∞ Hubbard model by treating the dynamical effects of local Hubbard correlations and disorder on an equal footing. This is achieved by a proper combination of the iterated perturbation theory and the coherent potential approximation. Within the paramagnetic phase, we find that the renormalized Fermi liquid metal phase of the pure Hubbard model is stable against disorder for small disorder strengths. With increasing disorder, strong resonant scattering effects destroy low-energy Fermi liquid coherence, leading to an {\it incoherent} metallic non-FL state off half-filling. Finally, for large enough disorder, a {\it continuous} transition to the Mott-Anderson insulating phase occurs. The nature of the non-FL metallic phase, as well as the effects of the low energy coherence (incoherence) on optical conductivity and electronic Raman spectra, are considered in detail.
We present a detailed, quantitative study of the competition between interaction- and disorder-induced effects in electronic systems. For this the Hubbard model with diagonal disorder (Anderson-Hubbard model) is investigated analytically and numerically in the limit of infinite spatial dimensions, i.e., within a dynamical mean-field theory, at half-filling. Numerical results are obtained for three different disorder distributions by employing quantum Monte Carlo techniques, which provide an explicit finite-temperature solution of the model in this limit. The magnetic phase diagram is constructed from the zeros of the inverse averaged staggered susceptibility. We find that at low enough temperatures and sufficiently strong interaction there always exists a phase with antiferromagnetic long-range order. A strong coupling anomaly, i.e., an increase of the N\'eel temperature for increasing disorder, is discovered. An explicit explanation is given, which shows that in the case of diagonal disorder this is a generic effect. The existence of metal-insulator transitions is studied by evaluating the averaged compressibility both in the paramagnetic and antiferromagnetic phases. A rich transition scenario, involving metal-insulator and magnetic transitions, is found and its dependence on the choice of the disorder distribution is discussed.
The influence of disorder and pseudogap fluctuations on the Mott insulator-metal transition in strongly correlated systems has been studied in the framework of the generalized dynamic mean field theory (DMFT + Σ approach). Using the results of investigations of the density of states (DOS) and optical conductivity, a phase diagram (disorder-Hubbard interaction-temperature) is constructed for the paramagnetic Anderson-Hubbard model, which allows both the effects of strong electron correlations and the influence of strong disorder to be considered. Strong correlations are described using the DMFT, while a strong disorder is described using a generalized self-consistent theory of localization. The DOS and optical conductivity of the paramagnetic Hubbard model have been studied in a pseudogap state caused by antiferromagnetic spin (or charge) short-range order fluctuations with a finite correlation length, which have been modeled by a static Gaussian random field. The effect of a pseudogap on the Mott insulator-metal transition has been studied. It is established that, in both cases, the static Gaussian random field (related to the disorder or pseudogap fluctuations) leads to suppression of the Mott transition, broadening of the coexistence region of the insulator and metal phases, and an increase in the critical temperature at which the coexistence region disappears.
Anderson-Hubbard Model in d=∞d = \inftyd=∞
We present a detailed, quantitative study of the competition between interaction- and disorder-induced effects in electronic systems. For this the Anderson-Hubbard model with diagonal disorder is investigated analytically and by Quantum Monte Carlo techniques in the limit of infinite spatial dimensions at half filling. We construct the magnetic phase diagram and find that at low enough temperatures and sufficiently strong interaction there always exists a phase with antiferromagnetic long-range order. A novel strong coupling anomaly, i.e.~an {\it increase} of the Néel-temperature for increasing disorder, is discovered and explained as an generic effect. The existence of metal-insulator transitions is studied by evaluating the averaged compressibility both in the paramagnetic and antiferromagnetic phase. A rich transition scenario, involving metal-insulator and magnetic transitions, is found and its dependence on the choice of the disorder distribution is discussed.
We study the paramagnetic Anderson-Hubbard model using an extension of dynamical mean field theory (DMFT), known as statistical DMFT, that allows us to treat disorder and strong electronic correlations on equal footing. An approximate nonlocal Green's function is found for individual disorder realizations and then configuration averaged. We apply this method to two-dimensional lattices with up to 1000 sites in the strong disorder limit, where an atomic-limit approximation is made for the self-energy. We investigate the scaling of the inverse participation ratio at quarter- and half-filling, and find a nonmonotonic dependence of the localization length on the interaction strength. For strong disorder, we do not find evidence for an insulator-metal transition, and the disorder potential becomes unscreened near the Mott transition. Furthermore, strong correlations suppress the Altshuler-Aronov density of states anomaly near half-filling.