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Journal of Experimental and Theoretical Physics

Peculiarities of the electron spectrum and metal-insulator transition in the strong correlation limit

V. Yu. Irkhin, Alexander V. Zarubin

Published May 1, 2013• 3 citations
Publisher

Abstract

Green’s function in the paramagnetic phase of the Hubbard model with strong electron correlations is calculated by the many-electron operators method. The density of states pattern is considered in the case of half-filling (metal-insulator transition) and in the doped case. The effect of the low-temperature Kondo scattering on the energy spectrum is analyzed, and the results are compared with the results of the dynamical mean-field theory (DMFT).

DOI
10.1134/s106377611305004x

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•Feb 27, 2020•0 citations
Green’s function in the paramagnetic phase of the Hubbard model with strong electron correlations is calculated by the many-electron operators method. The density of states pattern is considered in the case of half-filling (metal-insulator transition) and in the doped case. The effect of the low-temperature Kondo scattering on the energy spectrum is analyzed, and the results are compared with the results of the dynamical mean-field theory (DMFT).
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.
Correlated electrons in a binary alloy ${A}_{x}{B}_{1\ensuremath{-}x}$ are investigated within the Hubbard model and dynamical mean-field theory (DMFT). The random energies ${\ensuremath{\epsilon}}_{i}$ have a bimodal probability distribution and an energy separation $\ensuremath{\Delta}.$ We solve the DMFT equations by the numerical renormalization-group method at zero temperature and calculate the spectral density as a function of disorder strength $\ensuremath{\Delta}$ and interaction U at different fillings. For filling factors $\ensuremath{\nu}=x$ or 1+x1+x1+x the lower or upper alloy subband is half filled and the system becomes a Mott insulator at strong interactions, with a correlation gap at the Fermi level. At the metal-insulator transition hysteresis is observed. We also analyze the effective theory in the $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\Delta}}\ensuremath{\infty}$ limit and find good agreement between analytical and numerical results for the critical interaction Uc{U}_{c}Uc​ at which the metal-insulator transition occurs.
We address the nature of the Mott transition in the Hubbard model at half-filling using cluster dynamical mean field theory (DMFT). We compare cluster-DMFT results with those of single-site DMFT. We show that inclusion of the short-range correlations on top of the on-site correlations does not change the order of the transition between the paramagnetic metal and the paramagnetic Mott insulator, which remains first order. However, the short range correlations reduce substantially the critical U and modify the shape of the transition lines. Moreover, they lead to very different physical properties of the metallic and insulating phases near the transition point. Approaching the transition from the metallic side, we find an anomalous metallic state with very low coherence scale. The insulating state is characterized by the narrow Mott gap with pronounced peaks at the gap edge.
The density of states, the dynamic (optical) conductivity, and the phase diagram of the paramagnetic two-dimensional Anderson-Hubbard model with strong correlations and disorder are analyzed within the generalized dynamical mean field theory (DMFT + Σ approximation). Strong correlations are accounted by the DMFT, while disorder is taken into account via the appropriate generalization of the self-consistent theory of localization. We consider the two-dimensional system with the rectangular “bare” density of states (DOS). The DMFT effective single-impurity problem is solved by numerical renormalization group (NRG). The “correlated metal,” Mott insulator, and correlated Anderson insulator phases are identified from the evolution of the density of states, optical conductivity, and localization length, demonstrating both Mott-Hubbard and Anderson metal-insulator transitions in two-dimensional systems of finite size, allowing us to construct the complete zero-temperature phase diagram of the paramagnetic Anderson-Hubbard model. The localization length in our approximation is practically independent of the strength of Hubbard correlations. But the divergence of the localization length in a finite-size two-dimensional system at small disorder signifies the existence of an effective Anderson transition.
In this thesis, several aspects of correlation effects in band insulators that were hitherto not addressed, both in equilibrium and non-equilibrium, are studied using the Ionic Hubbard model (IHM) at half-filling and Dynamical mean-field theory (DMFT). The IHM is an extension of the Hubbard model on a bipartite lattice with a staggered on-site “ionic potential Δ added in. The Hubbard model by itself is a tight-binding model of electrons hopping between (orbitals localized on) lattice sites, with amplitudes t and t’ for first neighbor and second neighbor hopping respectively, together with a coulomb repulsion energy cost of U for double occupancy (i.e., with both up and down spin electrons) at any lattice site. The studies in this thesis address strong correlation effects in this model using DMFT techniques which map the lattice problem to a self consistently embedded quantum impurity problem. The impurity problem itself is solved using state of the art continuous time quantum monte-carlo (CTQMC) techniques (Ch.s 3 and 4) as well as the somewhat simpler Iterated Perturbation Theory (IPT) (Ch.s 3, 5 and 6). Chapter 3 of the thesis is devoted to a detailed analysis of the properties of the half-filled t-U-Δ IHM (i.e., with t’=0) on a Bethe lattice of infinite connectivity. It is shown conclusively here that for a finite Δ and at zero temperature (T=0), the IHM has a first order transition from the Band Insulator (BI) phase to an antiferromagnetic insulating (AFI) phase at a threshold U = UAF (which increases with Δ) such that the BI to AFI transition preempts the transition from the BI to the correlation induced paramagnetic metallic (PM) phase. Evidence is also presented for a quantum transition to a sliver of half-metal (HM) phase just after the AF order turns on, followed by a return to the AFI phase on further increasing U. With increasing T, the AF order is lost via a first-order transition for weak to intermediate U/t. In the strongly correlated regime, where the effective low-energy Hamiltonian is the Heisenberg model, the transition from the AFI to the paramagnetic Mott insulating phase (adiabatically connected to the BI phase) is of second order. As T increases, the range of U over which the AF order is stable shrinks, collapsing eventually to a line of tricritical points that separates the surfaces of first- and second-order phase transitions in the T-U-Δ space. In Chapter 4 of the thesis the t-t’-U-Δ IHM on a square lattice is studied using DMFT+CTQMC. It is shown here that the presence of t’ frustrates the AF order for weak to intermediate correlations, resulting in the stabilization of the correlation induced PM phase over a broad region of the parameter space, although the AFI is always the stable phase for large enough U. In the intermediate coupling regimes, two other interesting phases show up as a result of the competition among U, Δ and t’ : a Ferrimagnetic metallic (FM) phase which has non-zero values of the uniform as well as staggered magnetization; and even more interesting, an…