PACS 71.15.Mb, 71.27.+ a, 71.30.+ h Conventional band structure calculations in the local density approximation (LDA) [1 -3] are highly successful for many materials, but miss important aspects of the physics and energetics of strongly correlated electron systems, such as transition metal oxides and f-electron systems displaying, e.g., Mott insulating and heavy quasiparticle behavior. In this respect, the LDA + DMFT approach which merges LDA with a modern many-body approach, the dynamical mean-field theory (DMFT), has proved to be a breakthrough for the realistic modeling of correlated materials. Depending on the strength of the electronic correlation, a LDA + DMFT calculation yields the weakly correlated LDA results, a strongly correlated metal, or a Mott insulator. In this paper, the basic ideas and the set-up of the LDA + DMFT(X) approach, where X is the method used to solve the DMFT equations, are discussed. Results obtained with X = QMC (quantum Monte Carlo) and X = NCA (non-crossing approximation) are presented and compared, showing that the method X matters quantitatively. We also discuss LDA + DMFT results for two prime examples of correlated materials, i.e., V 2 O 3 and Ce which undergo a Mott -Hubbard metal -insulator and volume collapse transition, respectively.

We have studied the impact of non-local electronic correlations at all length scales on the MottHubbard metal-insulator transition in the unfrustrated two-dimensional Hubbard model. Combining dynamical vertex approximation, lattice quantum Monte-Carlo and variational cluster approximation, we demonstrate that scattering at long-range fluctuations, i.e., Slater-like paramagnons, opens a spectral gap at weak-to-intermediate coupling -irrespectively of the preformation of localized or short-ranged magnetic moments. This is the reason, why the two-dimensional Hubbard model has a paramagnetic phase which is insulating at low enough temperatures for any (finite) interaction and no Mott-Hubbard transition is observed. Introduction.The Mott-Hubbard metal-insulator transition (MIT) [1] is one of the most fundamental hallmarks of the physics of electronic correlations. Nonetheless, astonishingly little is known exactly, even for its simplest modeling, i.e., the single-band Hubbard Hamiltonian [2]: Exact solutions for this model are available only in the extreme, limiting cases of one and infinite dimensions.In one dimension (1D), the Bethe ansatz shows that there is actually no Mott-Hubbard transition [3][4][5]; or, in other words, it occurs for a vanishingly small Hubbard interaction U : At any U > 0 the 1D-Hubbard model is insulating at half filling. One dimension is, however, rather peculiar: While there is no antiferromagnetic ordering even at temperature T = 0, antiferromagnetic spin fluctuations are strong and long-ranged, decaying slowly, i.e., algebraically. Also the (doped) metallic phase is not a standard Fermi liquid but a Luttinger liquid.For the opposite extreme, infinite dimensions, the dynamical mean field theory (DMFT) [6] becomes exact [7], which allows for a clear-cut and -to a certain extentalmost "idealized" description of a pure Mott-Hubbard MIT. In fact, since in D = ∞ only local correlations survive [7], the Mott-Hubbard insulator of DMFT consists of a collection of localized (but not long-range ordered) magnetic moments. This way, if antiferromagnetic order is neglected or sufficiently suppressed, DMFT describes a first-order MIT [6,8], ending with a critical endpoint.As an approximation, DMFT is applicable to the more realistic cases of the three-and two-dimensional Hubbard models. However, the DMFT description of the MIT is the very same here, since only the non-interacting density of states (DOS) and in particular its second moment enter. This is a natural shortcoming of the mean-field nature of DMFT: antiferromagnetic fluctuations have no effect at all on the DMFT spectral function or self-energy above the antiferromagnetic ordering temperature T N .In 3D, antiferromagnetic fluctuations reduce T N siz-

A systematic investigation of the microscopic conditions stabilizing itinerant ferromagnetism of correlated electrons in a single-band model is presented. Quantitative results are obtained by quantum Monte Carlo simulations for a model with Hubbard interaction U and direct Heisenberg exchange interaction F within the dynamical mean-field theory. Special emphasis is placed on the investigation of (i) the distribution of spectral weight in the density of states, (ii) the importance of genuine correlations, and (iii) the significance of the direct exchange, for the stability of itinerant ferromagnetism at finite temperatures. We find that already a moderately strong peak in the density of states near the band edge suffices to stabilize ferromagnetism at intermediate U-values in a broad range of electron densities n. Correlation effects prove to be essential: Slater--Hartree-Fock results for the transition temperature are both qualitatively and quantitatively incorrect. The nearest-neighbor Heisenberg exchange does not, in general, play a decisive role. Detailed results for the magnetic phase diagram as a function of U, F, n, temperature T, and the asymmetry of the density of states are presented and discussed.Comment: 10 pages, 11 figures, RevTeX using epsf and multicol; shortened version, curve added in Fig. 2; to appear in Phys. Rev. B, Nov 15, 199

The anisotropic degenerate two-orbital Hubbard model is studied within dynamical mean-field theory at low temperatures. High-precision calculations on the basis of a refined quantum Monte Carlo (QMC) method reveal that two distinct orbital-selective Mott transitions occur for a bandwidth ratio of 2 even in the absence of spin-flip contributions to the Hund exchange. The second transition -not seen in earlier studies using QMC, iterative perturbation theory, and exact diagonalization -is clearly exposed in a low-frequency analysis of the self-energy and in local spectra. PACS numbers: 71.30.+h, 71.10.Fd, 71.27.+a The Mott-Hubbard metal-insulator transition -a nonperturbative correlation phenomenon -has been a subject of fundamental interest in solid state theory for decades. 1 Recently, this field became even more exciting by the discovery 2,3 of a two-step metal-insulator transition in the effective 3-band system Ca 2−x Sr x RuO 4 , for which the name orbital-selective Mott-transition (OSMT) was coined. 4 The Ca 2−x Sr x RuO 4 system was investigated theoretically in detail by Anisimov et al. 4 within the local density approximation (LDA and LDA+U) and within dynamical mean-field theory 5 (DMFT) solved using the non-crossing approximation (NCA). The underlying assumption of a correlation (rather than lattice-distortion) induced OSMT found support in further band structure calculations 6,7 and strong-coupling expansions for the localized electrons in the orbital-selective Mott phase. 8 Microscopic studies of the OSMT usually consider the 2-band Hubbard model H = H 1 + H 2 , wherehopping between nearest-neighbor sites i, j with amplitude t m for orbital m ∈ {1, 2}, intra-and interorbital Coulomb repulsion parametrized by U and U ′ , respectively, and Ising-type Hund's exchange coupling; n imσ = c † imσ c imσ for spin σ ∈ {↑, ↓}. In addition,contains spin-flip and pair-hopping terms (with1 ≡ 2, ↑ ≡↓ etc.). In cubic lattices, the Hamiltonian is invariant under spin rotation, J z = J ⊥ ≡ J; furthermore U ′ = U − 2J. In the following, we refer to H 1 + H 2 in this spin-isotropic case as the J-model and to the simplified Hamiltonian H 1 as the J z -model. Liebsch 9,10,11 questioned the OSMT scenario for Ca 2−x Sr x RuO 4 on the basis of finite-temperature quantum Monte Carlo (QMC) calculations (within DMFT) for the J z -model using J z = U/4, U ′ = U/2, and semielliptic "Bethe" densities of states with a bandwidth ratio W 2 /W 1 = 2. Additional studies using iterative perturbation theory (IPT) 11 seemed 12 to confirm his conclusion of a single Mott transition of both bands at the same critical U -value. Meanwhile, Koga et al. found an OSMT using exact diagonalization (ED), applied to the full J-model, 13 but not for the J z -model. 14 Consequently, the OSMT scenario was attributed to spin-flip and pairhopping processes.Very recently, four preprints appeared, 15,16,17,18 in which the OSMT was investigated in detail within the DMFT framework. Ref. 15 applied the Gutzwiller variational approach and ED to the J-model at...

The microscopic basis for the stability of itinerant ferromagnetism in correlated electron systems is examined. To this end several routes to ferromagnetism are explored, using both rigorous methods valid in arbitrary spatial dimensions, as well as Quantum Monte Carlo investigations in the limit of infinite dimensions (dynamical mean-field theory). In particular we discuss the qualitative and quantitative importance of (i) the direct Heisenberg exchange coupling, (ii) band degeneracy plus Hund's rule coupling, and (iii) a high spectral density near the band edges caused by an appropriate lattice structure and/or kinetic energy of the electrons. We furnish evidence of the stability of itinerant ferromagnetism in the pure Hubbard model for appropriate lattices at electronic densities not too close to half-filling and large enough U . Already a weak direct exchange interaction, as well as band degeneracy, is found to reduce the critical value of U above which ferromagnetism becomes stable considerably. Using similar numerical techniques the Hubbard model with an easy axis is studied to explain metamagnetism in strongly anisotropic antiferromagnets from a unifying microscopic point of view. 71.27.+a,75.10.Lp