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.
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.
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.
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.
We propose a way to identify strongly Hund-correlated materials by unveiling a key signature of Hund correlations at the two-particle level. The defining feature is the sign of the response of the frozen spin ratio (the long-time local spin-spin correlation function divided by the instantaneous value) under variation of electron density. The underlying physical reason is that the sign is closely related to the strength of charge fluctuations between the dominant atomic multiplets and higher-spin ones in a neighboring charge subspace. It is the predominance of these fluctuations that promotes Hund metallicity. The temperature dependence of the frozen spin ratio can further reveal a non-Fermi-liquid behavior and thus the Hund metal states. We analyze both degenerate and nondegenerate multiorbital Hubbard models and corroborate our argument by taking doped La2CuO4 and LaFeAsO as representative material examples, respectively, of Mott and Hund metals. Our proposal should be applicable to systems with non-half-filled integer electron fillings and their doped cases provided the doping drove the electron density toward the half filling.
Abstract: The metal–insulator transition (MIT) constitutes one of the most profound and persistent problems in condensed matter physics, sitting at the intersection of electronic structure theory, many-body physics, and emergent quantum phenomena. Conventional band theory, which successfully classifies materials as metals or insulators according to the filling of their electronic bands, fails dramatically when confronted with a class of compounds transition metal oxides chief among them that ought to be metallic by band-counting arguments yet are robustly insulating in the laboratory. The resolution of this paradox required abandoning the independent-electron picture entirely and recognizing that strong Coulomb repulsion between electrons can, by itself, drive localization. This insight, formalized by Mott and later distilled into the Hubbard model, established correlation-driven insulation as a phenomenon distinct from band insulation. The present paper offers a theoretical exploration of the MIT problem, tracing its conceptual development from the Mott criterion through the Hubbard Hamiltonian, the Brinkman–Rice scenario of quasiparticle mass divergence, and the watershed development of dynamical mean-field theory (DMFT), which rendered the Mott transition quantitatively tractable for the first time. We argue that the competition between the electronic bandwidth and the on-site interaction encoded in the ratio U/W provides the unifying organizing principle for the field. Building toward the modern frontier, we examine how the Mott transition connects to quantum phase transitions and quantum criticality, where zero-temperature instabilities governed by quantum rather than thermal fluctuations produce non-Fermi-liquid behavior and anomalous scaling. Case studies of vanadium oxides, rare-earth nickelates, and doped cuprates illustrate the diversity and subtlety of real correlated materials. We conclude that the MIT remains a central and unresolved problem whose continued study is increasingly entangled with the development of quantum materials and quantum technologies. Keywords: Metal–Insulator Transition; Mott Insulator; Strongly Correlated Electrons; Hubbard Model; DMFT; Quantum Criticality; Quantum Materials; Condensed Matter Physics
The Hund's coupling in multiorbital Hubbard systems induces spin freezing and associated Hund metal behavior. Using dynamical mean-field theory, we explore the effect of local moment formation, spin, and charge excitations on the entropy and specific heat of the three-orbital model. For fillings $2\ensuremath{\lesssim}n<3$ and low temperature, we demonstrate a substantial enhancement of the entropy in the spin-frozen metal phase to values comparable to the half-filled Mott insulator. We also discuss the appearance of entropy plateaus and peaks in the specific heat associated with the activation of spin and charge fluctuations at high temperature. The temperature scale for charge excitations is almost independent of filling and given by $\ensuremath{\approx}0.2U$, with U the intraorbital repulsion. Local spin excitations become relevant for filling n>1 and their characteristic temperature is proportional to the Hund coupling J, with a filling-dependent prefactor. The analysis of the specific heat in the atomic limit yields accurate predictions for these features in the strong-coupling regime.
Correlation-driven metal-insulator transitions and temperature-driven quantum-coherent-to-incoherent crossovers in correlated electron systems underpin the doping, temperature and frequency-resolved evolution of physical responses. Motivated by recent experimental studies that investigate the evolution of dynamical spin and charge responses, we analyze the spin and charge diffusion spectra in both half-filled and doped one-band Hubbard model using Dynamical Mean Field Theory (DMFT) combined with the Numerical Renormalization Group (NRG). We compare the relative strengths and limitations of Density Matrix NRG (DMNRG) and Full Density Matrix NRG (FDM-NRG) in capturing low-frequency spectral features and their evolution with temperature, interaction strength and band-filling. Key measures, including characteristic frequency scales, Kullback-Leibler divergence, diffusion constants, and kurtosis provide complementary but internally consistent picture for the evolution of spin and charge excitations across bandwidth as well as the band-filling driven Mott transitions and the coherent-incoherent crossover. We find that spin and charge fluctuations cross over from quantum-coherent-to-quantum-incoherent at distinct temperatures, providing a microscopic insight into the complex, two-stage, Fermi-to-non-Fermi liquid-to-bad metal crossovers seen in transport data, in particular in the dc resistivity.