Undoped iron-based superconductors accommodate six electrons in the five d-orbitals belonging to Fe-atom. It is nowadays well established that a correlated model at this filling is characterized by a bad metallic state induced by a sizable value of the Hund’s coupling J even when the Hubbard U becomes substantially larger than the bandwidth. Such systems are usually identified as Hund’s metal. This concept has been introduced to rationalize the observation that, in theoretical models of iron-based superconductors, ruthenates, and other materials, many relevant observables turn out to be remarkably dependent on Hund’s coupling J rather than on the Hubbard interaction U. In this thesis we gave some contributions to the understanding of this –still elusive– regime exploring different regimes of the incredibly rich physics of multi-orbital strongly correlated model.
Undoped iron-based superconductors accommodate six electrons in the five d-orbitals belonging to Fe-atom. It is nowadays well established that a correlated model at this filling is characterized by a bad metallic state induced by a sizable value of the Hund’s coupling J even when the Hubbard U becomes substantially larger than the bandwidth. Such systems are usually identified as Hund’s metal. This concept has been introduced to rationalize the observation that, in theoretical models of iron-based superconductors, ruthenates, and other materials, many relevant observables turn out to be remarkably dependent on Hund’s coupling J rather than on the Hubbard interaction U. In this thesis we gave some contributions to the understanding of this –still elusive– regime exploring different regimes of the incredibly rich physics of multi-orbital strongly correlated model.
For a long time strong electronic correlations in metals have mainly been associated with Mottness, the proximity to a Mott metal-insulator transition (MIT), where large Coulomb interactions induce the localization of charges. However, triggered by the discovery of the iron-based superconductors about ten years ago, it was realized that multi-orbital materials with only moderate Coulomb but sizeable Hund’s rule interactions – so-called Hund metals – allow for a distinct screening mechanism towards strong correlations: Hundness. Here, Hund’s rule constrains the spin rather than the charge dynamics. This discovery led to a vividly debated fundamental issue in the field of strongly correlated condensed matter systems, which is the main topic of the present thesis: what is the origin of strong correlations in the normal phase of Hund metals, Mottness or Hundness? And what are their decisive fingerprints? The goal of this dissertation is twofold. First, we present and advance our method: the numerical renormalization group (NRG) as viable real-frequency multi-band impurity solver for dynamical mean-field theory (DMFT), a common approach to tackle strongly correlated systems. Second, we apply DMFT+NRG to shed light on the Hund-metal problem raised above. In the first part of this thesis we present our state-of-the-art NRG solver, which offers direct access to data with unprecedented real-frequency spectral resolution at arbitrarily low energies and temperatures in contrast to commonly used Quantum Monte Carlo solvers. It is based on matrix product states and exploits non-abelian symmetries to reduce numerical costs. In the case of orbital symmetry, this allows us to treat multi-band models with more than two bands, and thus to tackle the Hund-metal problem for the first time with NRG. For multi-band models without orbital symmetry, an “interleaved” scheme of NRG (iNRG) was recently developed, dramatically increasing the numerical efficiency. Remarkably, the accuracy of iNRG is comparable to standard NRG, as we reveal in a detailed study. This finding establishes iNRG as a promising DMFT solver for material-specific model simulations. In the second part of this thesis we study a minimal toy model for Hund metals with DMFT+NRG, the orbital-symmetric three-band Hubbard-Hund model (3HHM) close to a lattice filling of 1/3. Our major insight is “spin-orbital separation” (SOS), a Hund’s-ruleinduced two-stage Kondo-type screening process, in which orbital screening occurs at much higher energies than spin screening. In Hund metals, i.e. far from a MIT phase boundary, SOS thus causes large electron masses by strongly reducing the coherence scale below which a Fermi liquid is formed. Further, it opens up a broad incoherent and strongly particle-hole asymmetric intermediate energy regime that reaches up to bare excitation scales. This SOS regime shows fractional power-law behavior and is characterized by resilient “Hund quasiparticles” with itinerant orbital degrees of freedom coupled non-trivially to quasi-free large spins. At zero temperature, the local density of states exhibits a two-tier quasiparticle peak on top of a broad incoherent background. In contrast, in Mott-correlated metals, i.e. close to the MIT phase boundary, the SOS regime becomes negligibly small and the Hubbard bands are well separated. These findings lead to distinct signatures of Hundness and Mottness in the temperature dependence of ARPES spectra, static local susceptibilities, resistivity, thermopower and entropy, many of which were also found in realistic simulations of the archetypal Hund- and Mott-correlated materials, Sr2RuO4 and V2O3. In summary, we provide evidence that and elucidate how Hundness evokes strong correlation effects in Hund metals. This might help to better interpret experimental results and guide superconducting theories.
The physics of many interesting correlated materials can be captured by multiorbital Hubbard models, where conduction electrons feature an additional orbital degree of freedom. The multiorbital characteristic is not a mere complication, but it leads to an immensely richer landscape of physical regimes. One of the key features is the interplay between Hubbard repulsion and Hund’s exchange coupling, which has been shown to lead to orbital-selective correlations and to the existence of correlation-resilient metals (usually called Hund’s metals) defying Mott localization. Here, we show that experimentally available platforms of SU(N)-symmetric ultracold atoms can indeed mimic the rich physics disclosed by multiorbital materials, by exploiting the internal degrees of freedom of multicomponent atoms. We discuss in detail the SU(N) version of interaction-resilient Hund’s metal and some other interesting regimes.
We study the finite-temperature properties of the half-filled two-band Hubbard model in the presence of Hund's rule coupling and orbital anisotropy. We use the mean-field treatment of the Z2 slave-spin theory with a finite-temperature extension of the zero-temperature gauge variable previously developed by Hassan and de' Medici [Phys. Rev. B 81, 035106 (2010)]. We consider the instability of the Fermi-liquid phases and how it is enhanced by the Hund's rule. We identify paramagnetic solutions that have zero quasiparticle weight with a bad metal, and the first-order transition temperature between the bad metal and the Fermi-liquid phase as a coherence temperature that signals the crossover to the bad metallic state. When orbital anisotropy is present, we found an intermediate transition to an orbital-selective bad metal (OSBM), where the narrow band becomes a bad metal while the wide band remains a renormalized Fermi liquid. The temperatures Tcoh and TOSBM at which the system transitions to the bad metal phases can be orders of magnitude less than the Fermi temperature associated with the noninteracting band. The parameter dependence of the temperature at which the OSBM is destroyed can be understood in terms of a ferromagnetic Kondo-Hubbard lattice model. In general, Hund's rule coupling enhances the bad metallic phases, reduces interorbital charge fluctuations, and increases spin fluctuations. The qualitative difference found in the ground state whether the Hund's rule is present or not, related to the degeneracy of the low-energy manifold, is also maintained for finite temperatures.
In the present thesis, we consider interaction induced instabilities in different electronic models consisting of multiple orbitals. We employ the functional renormalization group method, to tackle the many-particle problem. The main goal of this work is the identification of leading instabilities of different interacting electron systems and the relevant energy scales for the onset of correlations. First, we recapitulate the functional renormalization group formalism and discuss details of its application. We proceed with the investigation of two models, a continuum model and a model on a checkerboard lattice, which exhibit a single quadratic band crossing point at the Fermi level. Here, we find that electron-electron interactions can lead to ordering with non-trivial topological properties, i.e. the existence of topologically protected edge states. We further discuss the emergence of superconductivity, when the band crossing point is shifted away from the Fermi surface. Then, we turn to more realistic models featuring quadratic and cubic band crossing points, namely the honeycomb bi- and trilayer, which are used to describe the graphene layered systems. We obtain rich phase diagrams, with antiferromagnetic spin-density, two types of charge-density waves and a quantum spin Hall phase, which features in the case of the trilayer topologically protected edge states. With interaction parameters extracted from ab initio calculations, we observe a close competition between the antiferromagnetic and quantum spin Hall state. Here, the precise shape of the interaction decides which instability is the leading one. A comparison of the energy scales of the ordering phenomena in tri-, bi- and single layer reveals that when the interaction parameters from ab initio are appropriately rescaled, the functional renormalization group can qualitatively reproduce experimental gap sizes in the respective materials consistently. Afterwards, we study a multiband model of the copper-based unconventional superconductors. This is motivated by a puzzling material trend in copper-based high-Tc superconductors, pointed out by Pavarini et al. [PRL. 87, 047003 (2001)]: Compounds with larger next-nearest-neighbor hopping generally exhibit larger critical temperatures, which cannot be easily understood within spin-fluctuation theories of the one-band Hubbard model. Therefore, we consider the extension of the original model by including additional orbitals. We investigate a two-band model with an additional 4s orbital within a two-patch approximation and the N-patch-scheme. By this, a general understanding of the influence of the additional orbitals is established. Afterwards, we additionally include the 3dz2 orbital and show that the material trend, found in experiments, can, at least, qualitatively be reproduced. Lastly, we go back to the single band Hubbard model and examine the consequences of the widely used approximation of neglecting the self-energy and the frequency dependence of the interaction vertex. We establish that the phase diagram obtained from the functional renormalization group is only quantitatively affected. From this study, we conclude that neglecting self-energy and frequency dependence, is a sensible approach, in order to obtain a reliable qualitative picture of the low energy behavior of a weakly or moderately coupled system at reasonable expense.
We report a quantum phase transition between orbital-selective Mott states, with different localized orbitals, in a Hund's metals model. Using the density matrix renormalization group, the phase diagram is constructed varying the electronic density and Hubbard U, at robust Hund's coupling. We demonstrate that this transition is preempted by charge fluctuations and the emergence of free spinless fermions, as opposed to the magnetically driven Mott transition. The Luttinger correlation exponent is shown to have a universal value in the strong-coupling phase, whereas it is interaction dependent at intermediate couplings. At weak coupling we find a second transition from a normal metal to the intermediate-coupling phase.
For many years, strong electronic correlations in metals have mainly been associated with `Mottness' driven by the Coulomb repulsion, which suppresses charge fluctuations. Recently, `Hundness', induced by Hund's rule coupling that affects spin dynamics, has gained recognition as another route to strong correlations. Using dynamical mean-field theory and the numerical renormalization group, the authors identify numerous fingerprints distinguishing Hundness from Mottness in the temperature dependence of various physical quantities for a minimal model of Hund metals.