We present a new continuous-time solver for quantum impurity models such as those relevant to dynamical mean field theory. It is based on a stochastic sampling of a perturbation expansion in the impurity-bath hybridization parameter. Comparisons with Monte Carlo and exact diagonalization calculations confirm the accuracy of the new approach, which allows very efficient simulations even at low temperatures and for strong interactions. As examples of the power of the method we present results for the temperature dependence of the kinetic energy and the free energy, enabling an accurate location of the temperature-driven metal-insulator transition.

Strong electronic correlations are often associated with the proximity of a Mott insulating state. In recent years however, it has become increasingly clear that the Hund's rule coupling (intra-atomic exchange) is responsible for strong correlations in multi-orbital metallic materials which are not close to a Mott insulator. Hund's coupling has two effects: it influences the energetics of the Mott gap and strongly suppresses the coherence scale for the formation of a Fermi-liquid. A global picture has emerged recently, which emphasizes the importance of the average occupancy of the shell as a control parameter. The most dramatic effects occur away from half-filling or single occupancy. The theoretical understanding and physical properties of these 'Hund's metals' are reviewed, together with the relevance of this concept to transition-metal oxides of the 3d, and especially 4d series (such as ruthenates), as well as to the iron-based superconductors (iron pnictides and chalcogenides).

We show that electron- and hole-doped BaFe(2)As(2) are strongly influenced by a Mott insulator that would be realized for half-filled conduction bands. Experiments show that weakly and strongly correlated conduction electrons coexist in much of the phase diagram, a differentiation which increases with hole doping. This selective Mottness is caused by the Hund's coupling effect of decoupling the charge excitations in different orbitals. Each orbital then behaves as a single-band doped Mott insulator, where the correlation degree mainly depends on how doped is each orbital from half filling. Our scenario reconciles contrasting evidences on the electronic correlation strength, implies a strong asymmetry between hole and electron doping, and establishes a deep connection with the cuprates.

We show that in multi-band metals the correlations are strongly affected by the Hund's rule coupling, which depending on the filling promotes metallic, insulating or bad-metallic behavior. The quasiparticle coherence and the proximity to a Mott insulator are influenced distinctly and, away from single-and half-filling, in opposite ways. A strongly correlated bad-metal far from a Mott phase is found there. We propose a concise classification of 3d and 4d transition-metal oxides within which the ubiquitous occurrence of strong correlations in Ru-and Cr-based oxides, as well as the recently measured high Néel temperatures in Tc-based perovskites are naturally explained.Hund's rules determine the ground-state of an isolated atom by accounting for the dependence of the Coulomb repulsion between electrons on their relative spin and orbital configurations. In insulating solids, their role is to select the relevant atomic multiplets, which are then coupled by inter-site magnetic interactions. In contrast, the effects of the Hund's rule coupling in metallic compounds are less understood. The difficulty lies in dealing with the localized (atomic) and itinerant characters of electrons on equal footing, a key issue for materials with strong electron correlations [1]. Despite increasing awareness of the physical relevance of the Hund's rule coupling for such materials [2][3][4][5][6][7][8], a global view is still lacking.In this article, we fill this gap and provide a classification with respect to the number of electrons filling the active orbitals. We show that, aside from the case of a singly-occupied shell (where metallicity is favored [4,8]), or a half-filled shell (where it promotes Mott insulating behaviour [9,10]) the Hund's rule coupling induces conflicting tendencies and thus causes strong correlations far from the insulating state ('bad-metal' behavior). This picture explains the observed physical properties of a number of transition-metal oxides and allows for predictions on novel ones, such as Technetium compounds.In order to describe all these possibilities and illustrate our key-point in a simple context, we consider a model of three identical bands with semicircular density-of-states of half-bandwidth D filled by N electrons per site. This is relevant, for example, to transition-metal oxides with cubic symmetry and a partially filled t 2g shell well separated from the empty e g shell. The standard interaction Hamiltonian [1] can be written as:whereN denotes total charge, S spin and T the angular momentum operators. U is the intra-orbital interaction and J is the Hund's rule coupling. The Hund's rule coupling favors, in decreasing order: configurations with parallel spins in different orbitals, with parallel spins in the same orbital, and with opposite spins in the same orbital, maximizing S and then T . We solve the model using dynamical mean-field theory (DMFT) [11] which maps a correlated electron system onto a quantum-impurity problem: an effective atom coupled to a self-consistent environment. This approa...

We outline a general mechanism for orbital-selective Mott transition, the coexistence of both itinerant and localized conduction electrons, and show how it can take place in a wide range of realistic situations, even for bands of identical width and correlation, provided a crystal field splits the energy levels in manifolds with different degeneracies and the exchange coupling is large enough to reduce orbital fluctuations. The mechanism relies on the different kinetic energy in manifolds with different degeneracy. This phase has Curie-Weiss susceptibility and non-Fermi-liquid behavior, which disappear at a critical doping, all of which is reminiscent of the physics of the pnictides.

We examine whether the Mott transition of a half-filled, two-orbital Hubbard model with unequal bandwidths occurs simultaneously for both bands or whether it is a two-stage process in which the orbital with narrower bandwith localizes first (giving rise to an intermediate 'orbital-selective' Mott phase). This question is addressed using both dynamical mean-field theory, and a representation of fermion operators in terms of slave quantum spins, followed by a mean-field approximation (similar in spirit to a Gutzwiller approximation). In the latter approach, the Mott transition is found to be orbital-selective for all values of the Coulomb exchange (Hund) coupling J when the bandwidth ratio is small, and only beyond a critical value of J when the bandwidth ratio is larger. Dynamical mean-field theory partially confirms these findings, but the intermediate phase at J = 0 is found to differ from a conventional Mott insulator, with spectral weight extending down to arbitrary low energy. Finally, the orbital-selective Mott phase is found, at zero-temperature, to be unstable with respect to an inter-orbital hybridization V , and replaced at small V by a state with a large effective mass (and a low quasiparticle coherence scale) for the narrower band.

We study how a finite hybridization between a narrow correlated band and a wide conduction band affects the Mott transition. At zero temperature, the hybridization is found to be a relevant perturbation, so that the Mott transition is suppressed by Kondo screening. In contrast, a first-order transition remains at finite temperature, separating a local-moment phase and a Kondo-screened phase. The first-order transition line terminates in two critical end points. Implications for experiments on f-electron materials such as the cerium alloy Ce0.8La0.1Th0.1 are discussed.

We show how in multi-band materials, the Hund's coupling plays a crucial role in tuning the degree of electronic correlation. While in half-filled systems it enhances the correlations, in all other cases it pushes the boundary for the Mott transition at very high critical couplings. Moreover in weakly-hybridized non-degenerate systems the Hund's coupling plays the role of band-decoupler, causing a change from a collective to an individual band behavior, due to the freezing of orbital fluctuations. In this situation the physics is strongly dependent on individual filling and electronic structure of each band, and orbital-selective Mott transitions (or even a cascade of such transitions) are to be expected. More generally a heavy differentiation in the actual degree of correlation of different bands arises and the system can show both weakly and strongly correlated electrons.