The calculation of the electronic properties of materials is an important task of solid-state theory, albeit particularly difficult if electronic correlations are strong, e.g., in transition metals, their oxides and in f-electron systems. The standard approach to material calculations, the density functional theory in its local density approximation (LDA), incorporates electronic correlations only very rudimentarily and fails if the correlations are strong. Encouraged by the success of dynamical mean field theory (DMFT) in dealing with strongly correlated model Hamiltonians, physicists from the bandstructure and the many-body communities have joined forces and developed a combined LDA + DMFT method recently. Depending on the strength of electronic correlations, this new approach yields a weakly correlated metal as in the LDA, a strongly correlated metal or a Mott insulator. This approach is widely regarded as a breakthrough for electronic structure calculations of strongly correlated materials. We review ...

Electronic structure calculations using dynamical mean field theory

We investigate the Mott transitions in two-band Hubbard models with different bandwidths. Applying dynamical mean field theory, we discuss the stability of itinerant quasiparticle states in each band. We demonstrate that separate Mott transitions occur at different Coulomb interaction strengths in general, which merge to a single transition only under special conditions. This kind of behavior may be relevant for the physics of the single-layer ruthenates, Ca2-xSrxRuO4.

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Orbital-selective Mott transitions in the degenerate Hubbard model

Quantum phase transitions in metals are often accompanied by violations of Fermi liquid behavior in the quantum critical regime. Particularly fascinating are transitions beyond the Landau-Ginzburg-Wilson concept of a local order parameter. The breakdown of the Kondo effect in heavy-fermion metals constitutes a prime example of such a transition. Here, the strongly correlated f electrons become localized and disappear from the Fermi surface, implying that the transition is equivalent to an orbital-selective Mott transition, as has been discussed for multi-band transition-metal oxides. In this article, available theoretical descriptions for orbital-selective Mott transitions will be reviewed, with an emphasis on conceptual aspects like the distinction between different low-temperature phases and the structure of the global phase diagram. Selected results for quantum critical properties will be listed as well. Finally, a brief overview is given on experiments which have been interpreted in terms of orbital-selective Mott physics.

Orbital-Selective Mott Transitions: Heavy Fermions and Beyond

We revisit a problem of theoretical description of alpha-iron. By performing LDA+DMFT calculations in the paramagnetic phase we find that Coulomb interaction and, in particular Hund exchange, yields the formation of local moments in e_g electron band, which can be traced from imaginary time dependence of the spin-spin correlation function. This behavior is accompanied by non-Fermi-liquid behavior of e_g electrons and suggests using local moment variables in the effective model of iron. By investigating orbital-selective contributions to the Curie-Weiss law for Hund exchange I=0.9 eV we obtain an effective value of local moment of e_g electrons 2p=1.04 mu_B. The effective bosonic model, which allows to describe magnetic properties of iron near the magnetic phase transition, is proposed.

Orbital-selective formation of local moments in α -iron: First-principles route to an effective model

Starting with an extended version of the Anderson lattice where the $f$ electrons are allowed a weak dispersion, we examine the possibility of a Mott localization of the $f$ electrons for a finite value of the hybridization $V$. We study the fluctuations at the quantum critical point (QCP) where the $f$ electrons localize. We find that they are in the same universality class as for the Kondo breakdown QCP, with the following notable features. The quantum critical regime sees the appearance of an additional energy scale separating two universality classes. In the low energy regime, the fluctuations are dominated by massless gauge modes, while in the intermediate energy regime, the fluctuations of the modulus of the order parameter are the most relevant ones. In the latter regime, electric transport simplifies drastically, leading to a quasilinear resistivity in three dimensional and anomalous exponents lower than $T$ in two dimensional. This rather unique feature of the quantum critical regime enables us to make experimentally testable predictions.

Selective Mott transition and heavy fermions

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\char22{}not seen in earlier studies using QMC, iterative perturbation theory, and exact diagonalization\char22{}is clearly exposed in a low-frequency analysis of the self-energy and in local spectra.

/pdf/orbital-selective-mott-transitions-in-the-anisotropic-two-21nppemal8.pdf

Orbital-selective Mott transitions in the anisotropic two-band Hubbard model at finite temperatures

In a Comment [cond-mat/0506138] on our recent e-print [cond-mat/0505106] Liebsch claimed "excellent correspondence" between our high-precision quantum Monte-Carlo (QMC) data for the anisotropic two-band Hubbard model with Ising type exchange couplings and his earlier QMC results. Liebsch also claimed that the sequence of two orbital-selective Mott transitions, identified by us in this model, had already been reported in his earlier work. Here we demonstrate that both claims are incorrect. We establish that Liebsch's previous QMC estimates for the quasiparticle weight Z have relative errors exceeding 100% near transitions and cannot be used to infer the existence of a second Mott transition (for U_{c2}~2.5). We further show that Liebsch's attribution of our findings to his own earlier work is disproved by the published record. Consequently, the Comment is unwarranted; all results and formulations of our e-print remain valid.

Reply to "Comment on `Orbital-selective Mott transitions in the anisotropic two-band Hubbard model at finite temperatures'"

Using high-precision quantum Monte Carlo (QMC) simulations within the framework of dynamical mean field theory (DMFT), we show that the anisotropic degenerate two-orbital Hubbard model contains two consecutive orbital-selective Mott transitions (OSMTs) even in the absence of spin-flip terms and pair-hopping processes. In order to reveal the second transition we carefully analyze the low-frequency part of the self-energy and the local spectral functions. This paper extends our previous work to lower temperatures. We discuss the nature - in particular the order - of both Mott transitions and list various possible extensions.

https://arxiv.org/pdf/cond-mat/0507682.pdf

Orbital-selective Mott transitions in the 2-band J_z-model: a high-precision quantum Monte Carlo study

Orbital-selective Mott transitions in the 2-band Jz-model : a high-precision quantum Monte Carlo study

Using quantum Monte Carlo (QMC) simulations we determine the magnetic phase diagram of the anisotropic two-band Hubbard model within the dynamical mean-field theory (DMFT) in the important intermediate-coupling regime. We compare the QMC predictions with exact results from second-order weak-and strong-coupling perturbation theory. We find that the orbital-selective Mott transition (OSMT), which occurs in the fully frustrated case, is completely hidden in the antiferromagnetic (AF) ground state of the model. On the basis of our results, we discuss possible mechanisms of frustration. We also demonstrate the close relationship of the physics of the two-band Hubbard model in the orbital-selective Mott (OSM) phase to the Falicov-Kimball model.

C. Knecht

Papers

Orbital-selective Mott transitions in the anisotropic two-band Hubbard model at finite temperatures

Reply to "Comment on `Orbital-selective Mott transitions in the anisotropic two-band Hubbard model at finite temperatures'"

Orbital-selective Mott transitions in the 2-band J_z-model: a high-precision quantum Monte Carlo study

Orbital-selective Mott transitions in the 2-band Jz-model : a high-precision quantum Monte Carlo study

Magnetic phase diagram of the anisotropic multi-band Hubbard model