Luca de' Medici

Continuous-Time Solver for Quantum Impurity Models

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 Correlations from Hund’s Coupling

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 multiorbital metallic materials that 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. We review the theoretical understanding and physical properties of these Hund’s metals, together with the relevance of this concept to transition-metal oxides (TMOs) of the 3d, and especially 4d, series (such as ruthenates), as well as to the iron-based superconductors (iron pnictides and chalcogenides).

Orbital-selective Mott transition out of band degeneracy lifting.

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.

Optical conductivity and the correlation strength of high-temperature copper-oxide superconductors

High-temperature superconductors are difficult to model because most conventional theories fail for the strong repulsive interactions between electrons. But what if the correlations are not as strong as believed? Perhaps the magnetic correlations are more essential. Since their discovery in 1986, the high-temperature copper-oxide superconductors have been a central object of study in condensed-matter physics. Their highly unusual properties are widely (although not universally) believed to be a consequence of electron–electron interactions that are so strong that the traditional paradigms of condensed-matter physics do not apply: instead, entirely new concepts and techniques are required to describe the physics. In particular, the superconductivity is obtained by adding carriers to insulating ‘parent compounds’. These parent compounds have been identified1 as ‘Mott’ insulators, in which the lack of conduction arises from anomalously strong electron–electron repulsion. The unusual properties of Mott insulators are widely2 believed to be responsible for the high-temperature superconductivity. Here, we present a comparison of new theoretical calculations and published3,4,5,6,7,8 optical conductivity measurements, which challenges this belief. The analysis indicates that the correlation strength in the cuprates is not as strong as previously believed, in particular that the materials are not properly regarded as Mott insulators. Rather, antiferromagnetism seems to be necessary to obtain the insulating state. By implication, antiferromagnetism is essential to the properties of the doped metallic and superconducting state as well.

Hund’s coupling and its key role in tuning multiorbital correlations

We show how in multi-band materials, the Hunds 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 Hunds 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.

Solving the dynamical mean-field theory at very low temperatures using the Lanczos exact diagonalization

We present an efficient method to solve the impurity Hamiltonians involved in Dynamical Mean-Field Theory at low but finite temperature, based on the extension of the Lanczos algorithm from ground state properties alone to excited states. We test the approach on the prototypical Hubbard model and find extremely accurate results from T=0 up to relatively high temperatures, up to the scale of the critical temperature for the Mott transition. The algorithm substantially decreases the computational effort involved in finite temperature calculations.

Covalency, double-counting, and the metal-insulator phase diagram in transition metal oxides

Dynamical mean field theory calculations are used to show that for late transition metal oxides a critical variable for the Mott/charge-transfer transition is the number of d electrons, which is determined by charge transfer from oxygen ions. Insulating behavior is found only for a narrow range of d occupancy, irrespective of the size of the intra-d Coulomb repulsion. The result is useful in interpreting “density functional + U ” and “density functional plus dynamical mean field” methods in which additional correlations are applied to a specific set of orbitals and an important role is played by the “double counting correction” which dictates the occupancy of these correlated orbitals. General considerations are presented and are illustrated by calculations for two representative transition metal oxide systems: layered perovskite Cu-based high-Tc materials, an orbitally nondegenerate electronically quasi-two-dimensional system, and pseudocubic rare earch nickelates, an orbitally degenerate electronically three-dimensional system. Density functional calculations yield d occupancies very far from the Mott metal-insulator phase boundary in the nickelate materials, but closer to it in the cuprates, indicating the sensitivity of theoretical models of the cuprates to the choice of double counting correction, and corroborating the critical role of lattice distortions in attaining the experimentally observed insulating phase in the nickelates.

Genesis of Coexisting Itinerant and Localized Electrons in Iron Pnictides

We show how the general features of the electronic structure of the Fe-based high-Tc superconductors are a natural setting for a selective localization of the conduction electrons to arise. Slave-spin and dynamical mean-field calculations support this picture and allow for a comparison of the magnetic properties with experiments.

Role of oxygen-oxygen hopping in the three-band copper-oxide model: Quasiparticle weight, metal insulator and magnetic phase boundaries, gap values, and optical conductivity

We investigate the effect of oxygen-oxygen hopping on the three-band copper-oxide model relevant to high-Tc cuprates, finding that the physics is changed only slightly as the oxygen-oxygen hopping is varied. The location of the metal-insulator phase boundary in the plane of interaction strength and charge-transfer energy shifts by ∼0.5 eV or less along the charge-transfer axis, the quasiparticle weight has approximately the same magnitude and doping dependence, and the qualitative characteristics of the electron-doped and hole-doped sides of the phase diagram do not change. The results confirm the identification of La2CuO4 as a material with an intermediate correlation strength. However, the magnetic phase boundary as well as higher energy features of the optical spectrum are found to depend on the magnitude of the oxygen-oxygen hopping. We compare our results to previously published one-band and three-band model calculations.

Antiferromagnetism and the gap of a Mott insulator: Results from analytic continuation of the self-energy

Direct analytic continuation of the self-energy is used to determine the effect of antiferromagnetic ordering on the spectral function and optical conductivity of a Mott insulator. Comparison of several methods shows that the most robust estimation of the gap value is obtained by use of the real part of the continued self-energy in the quasiparticle equation within the single-site dynamical mean-field theory of the two-dimensional square lattice Hubbard model, where, for a