The generalized Hubbard model is an important theoretical model for modeling strongly correlated materials. To be able to theoretically predict the properties of the materials, the model requires Hubbard's $U$ and Hund's $J$ parameter that represent the on-site Coulomb and exchange interaction, respectively. For bare Coulomb interactions, the analytic expression of $U$ and $J$ are analytically described by Racah's $A,B,C$ parameters. However, the values of $U$ are too large for transition-metal-based materials. To obtain more accurate values for realistic materials, we employ a Yukawa-type screened Coulomb interaction, characterized by screening constant $λ$. We characterize $λ$ for transition metals. The modified $A,B,C$ parameters give a more realistic $U$ and $J$ values.
We study the interplay between Mott physics, driven by Coulomb repulsion U, and Hund physics, driven by Hund's coupling J, for a minimal model for Hund metals, the orbital-symmetric three-band Hubbard-Hund model (3HHM) for a lattice filling of 1/3. Hund-correlated metals are characterized by spin-orbital separation (SOS), a Hund's-rule-induced two-stage Kondo-type screening process, in which spin screening occurs at much lower energy scales than orbital screening. By contrast, in Mott-correlated metals, lying close to the phase boundary of a metal-insulator transition, the SOS window becomes n…
The generalized spin-one-half Falicov-Kimball model with Hund and Hubbard coupling is used to examine effects of spin ordering on superconducting correlations in the strongly correlated electron and spin systems. It is found that the ferromagnetic spin clusters (lines, bands, domains) suppress the superconducting correlations in the d-wave chanel, while the antiferromagnetic ones have the fully opposite effect. The enhancement of the superconducting correlations due to the antiferromagnetic spin ordering is by factor 3 in the axial striped phase and even by the factor 8 in the phase segregated…
We investigate the phase diagram of the spin-orbit-coupled three orbital Hubbard model at arbitrary filling by means of dynamical mean-field theory combined with continuous-time quantum Monte Carlo. We find that the spin-freezing crossover occurring in the metallic phase of the non-relativistic multiorbital Hubbard model can be generalized to a $\mathbf{J}$-freezing crossover, with $\mathbf{J}=\mathbf{L}+\mathbf{S}$, in the spin-orbit-coupled case. In the $\mathbf{J}$-frozen regime the correlated electrons exhibit a non-trivial flavor selectivity and energy dependence. Furthermore, in the regi…
Hund metals are multi-orbital systems with moderate Coulomb interaction, $U$, and sizeable Hund's rule coupling, $J<U$, that aligns the spins in different orbitals. They show strong correlation effects, like very low Fermi-liquid coherence scales and intriguing incoherent transport regimes, resulting in bad metallic behavior. But to what extent are these strong correlations governed by Mottness, i.e. the blocking of charge fluctuations close to a Mott insulator transition (MIT) induced by $U$, or by Hundness, a new route towards strong correlations induced by $J$? To answer this question, we s…
In the study of strongly-correlated, many-electron systems, the Hubbard Kanamori (HK) model has emerged as one of the prototypes for transition metal oxide physics. The model is multi-band in nature and contains Hund's coupling terms, which have pronounced effects on metal-insulator transitions, high-temperature superconductivity, and other physical properties. In the following, we present a complete theoretical framework for treating the HK model using the ground state Auxiliary Field Quantum Monte Carlo (AFQMC) method and analyze its performance on few-band models whose parameters approximat…
While excitonic instabilities in multiorbital systems recently have come under scrutiny in a variety of transition-metal compounds, understanding emergence of these instabilities from strong electronic interactions has remained a challenge. Here, we present a sign-problem-free determinant quantum Monte Carlo study of excitonic density orders in a half-filled two-orbital Hubbard-Kanamori model with broken orbital degeneracy, which accounts for the role of Hund's coupling in transition-metal compounds. For strong inverted (negative) Hund's exchange, we find numerical evidence for the emergence o…
Projector Quantum-Monte-Carlo Method is used to examine effects of the spin-independent $U_{fd}$ as well as spin-dependent $J_z$ Coulomb interaction between the localized $f$ and itinerant $d$ electrons on the stability of various types of charge/spin ordering and superconducting correlations in the spin-one-half Falicov-Kimball model with Hund and Hubbard coupling. The model is studied for a wide range of $f$ and $d$-electron concentrations and it is found that the interband interactions $U_{fd}$ and $J_z$ stabilize three basic types of charge/spin ordering, and namely, (i) the axial striped …
An antiferromagnetic Hund coupling in multiorbital Hubbard systems induces orbital freezing and an associated superconducting instability, as well as unique composite orders in the case of an odd number of orbitals. While the rich phase diagram of the half-filled three-orbital model has recently been explored in detail, the properties of the doped system remain to be clarified. Here, we complement the previous studies by computing the entropy of the half-filled model, which exhibits an increase in the orbital-frozen region, and a suppression in the composite ordered phase. The doping dependent…
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 $Z_2$ slave-spin theory with a finite-temperature extension of the zero-temperature gauge variable previously developed by Hassan and de' Medici http://dx.doi.org/10.1103/PhysRevB.81.035106}{Phys. Rev. B {\bf 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 quasi-particle weight with bad me…
Mott-Hubbard and Hund electron correlations have been realized thus far in separate classes of materials. Here, we show that a single moiré homobilayer encompasses both kinds of physics in a controllable manner. We develop a microscopic multiband model that we solve by dynamical mean-field theory to nonperturbatively address the local many-body correlations. We demonstrate how tuning with twist angle, dielectric screening, and hole density allows us to switch between Mott-Hubbard and Hund correlated states in a twisted WSe$_2$ bilayer. The underlying mechanism is based on controlling Coulomb-i…
In this work, we report the pressure dependence of the effective Coulomb interaction parameters (Hubbard U) in paramagnetic NiO within the constrained random phase approximation (cRPA). We consider five different low energy models starting from the most expensive one that treats both Ni-d and O-p states as correlated orbitals (dp-dp model) to the smallest possible two-orbital model comprising the eg states only (eg-eg model). We find that in all the considered models, the bare interactions are not very sensitive to the compression. However the partially screened interaction parameters show an …
We study the relaxation dynamics of photo-carriers in the paramagnetic Mott insulating phase of the half-filled two-band Hubbard model. Using nonequilibrium dynamical mean field theory, we excite charge carriers across the Mott gap by a short hopping modulation, and simulate the evolution of the photo-doped population within the Hubbard bands. We observe an ultrafast charge-carrier relaxation driven by emission of local spin excitations with an inverse relaxation time proportional to the Hund's coupling. The photo-doping generates additional side-bands in the spectral function, and for strong …
We study the doping-driven Mott metal-insulator transition for multi-orbital Hubbard models with Hund's exchange coupling at finite temperatures. As in the single-orbital Hubbard model, the transition is of first-order within dynamical mean field theory, with a coexistence region where two solutions can be stabilized. We find, that in the presence of finite Hund's coupling, the insulating phase is connected to a badly metallic phase, which extends to surprisingly large dopings. While fractional power-law behavior of the self-energies on the Matsubara axis is found on both sides of the transiti…
We study the ground state of the Hubbard model on a square lattice with two degenerate orbitals per site and at integer fillings as a function of onsite Hubbard repulsion $U$ and Hund's intra-atomic exchange coupling $J$. We use a variational slave-spin mean field (VSSMF) method which allows symmetry broken states to be studied within the computationally less intensive slave-spin mean field formalism, thus making the method more powerful to study strongly correlated electron physics. The results show that at half-filling, the ground state at smaller $U$ is a Slater antiferromagnet (AF) with su…
The Hund 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. In particular, we demonstrate a substantial enhancement of the entropy in the spin-frozen metal phase at low temperatures, and peaks in the specific heat associated with the activation of spin and charge fluctuations at high temperature. We also clarify how these temperature scales depend on the interaction parameters…
The density functional theory (DFT)+$U$ method is a pragmatic and effective approach for calculating the ground-state properties of strongly-correlated systems, and linear response calculations are widely used to determine the requisite Hubbard parameters from first principles. We provide a detailed treatment of spin within this linear response approach, demonstrating that the conventional Hubbard $U$ formula, unlike the conventional DFT+$U$ corrective functional, incorporates interactions that are off-diagonal in the spin indices and places greater weight on one spin channel over the other. W…
We explore the transition to a charge-disproportionated insulating phase in a five-orbital cubic tight-binding model applicable to transition-metal perovskites with a formal $d^4$ occupation of the transition-metal cation, such as ferrates or manganites. We use dynamical mean-field theory to obtain the phase diagram as a function of the average local Coulomb repulsion $U$ and the Hund's coupling $J$. The main structure of the phase diagram follows from the zero band-width (atomic) limit and represents the competition between high-spin and low-spin homogeneous and an inhomogeneous charge-dispro…
A comparative density functional plus dynamical mean field theory study of the pseudocubic ruthenate materials CaRuO$_3$ and SrRuO$_3$ is presented. Phase diagrams are determined for both materials as a function of Hubbard repulsion $U$ and Hund's rule coupling $J$. Metallic and insulating phases are found, as are ferromagnetic and paramagnetic states. The locations of the relevant phase boundaries are determined. Based on the computed phase diagrams, Mott-dominated and Hund's dominated regimes of strong correlation are distinguished. Comparison of calculated properties to experiments indicate…
Titanium dioxide (TiO$_2$) presents a long-standing challenge for approximate Kohn-Sham density-functional theory (KS-DFT), as well as to its Hubbard-corrected extension, DFT+$U$. We find that a previously proposed extension of first-principles DFT+$U$ to incorporate a Hund's $J$ correction, termed DFT+$U$+$J$, in combination with parameters calculated using a recently proposed linear-response theory, predicts fundamental band-gaps accurate to well within the experimental uncertainty in rutile and anatase TiO$_2$. Our approach builds upon established findings that Hubbard correction to both ti…
Motivated by the recent discovery of superconductivity in infinite-layer nickelates RE$_{1-δ}$Sr$_δ$NiO$_2$ (RE$=$Nd, Pr), we study the role of Hund's coupling $J$ in a quarter-filled two-orbital Hubbard model which has been on the periphery of the attention. A region of negative effective Coulomb interaction of this model is revealed to be differentiated from three- and five-orbital models in their typical Hund's metal active fillings. We identify distinctive regimes including four different correlated metals, one of which stems from the proximity to a Mott insulator while the other three, wh…
We analyze two different fermionic systems that defy Mott localization showing a metallic ground state at integer filling and very large Coulomb repulsion. The first is a multiorbital Hubbard model with a Hund's coupling, where this physics has been widely studied and the new metallic state is called a Hund's metal, and the second is a SU(3) Hubbard model with a patterned single-particle potential designed to display a similar interaction-resistant metal in a set-up which can be implemented with SU($N$) ultracold atoms. With simple analytical arguments and exact numerical diagonalization of th…
Revealing Hund superdispersion with tunneling spectroscopy
University of St Andrews（圣安德鲁斯大学）；University of Cologne（科隆大学）；Flatiron Institute（平顿研究所）；Université Paris-Saclay（巴黎萨克雷大学）；Max Planck Institute for Chemical Physics of Solids（马克斯·普朗克固体化学物理研究所）；Collège de France（法兰西公学院）；Ecole Polytechnique（巴黎综合理工学院）；Université de Genève（日内瓦大学）
Motivated by the realization of spin-valley Hubbard on triangular moiré superlattice in ABC trilayer graphene aligned with hexagon boron nitride (hBN) and possibly also in twisted transition metal dichalcogenide homobilayers, we study possible Mott insulating phases and pseudogap metals based on symmetry constraint and parton mean field theories. First we show that Luttinger constraint allows two distinct symmetric and featureless Fermi liquids when there is an inter-valley Hund's term breaking $SU(4)$ spin rotation. Especially, there exists a symmetric and featureless "pseudogap metal" with s…
The theory of correlated electron systems on a lattice proves notoriously complicated because of the exponential growth of Hilbert space. Mean-field approaches provide valuable insight when the self-energy has a dominant local structure. Additionally, the extraction of effective low-energy theories from the generalized many-body representation is highly desirable. In this respect, the rotational-invariant slave boson (RISB) approach in its mean-field formulation enables versatile access to correlated lattice problems. However in its original form, due to numerical complexity, the RISB approach…
