By connecting Hund's physics with flat band physics, we establish an exact result for studying ferromagnetism in a multiorbital system. We consider a two-layer model consisting of a $p_x$, $p_y$-orbital honeycomb lattice layer and an $f$-orbital triangular lattice layer with sites aligned with the centers of the honeycomb plaquettes. The system features a flat band that admits a percolation representation for an appropriate chemical potential difference between the two layers. In this representation, the ground state space is spanned by maximum-spin clusters of localized single-particle states, and averaging over the ground states yields a correlated percolation problem with weights due to the spin degeneracy of the clusters. A paramagnetic-ferromagnetic transition occurs as the band approaches half filling and the ground states become dominated by states with a large maximum-spin cluster, as shown by Monte Carlo simulation.
Hund's pairing refers to Cooper pairing generated by onsite interactions that become attractive due to large Hund's exchange $J$. This is possible in multiorbital systems even when all local bare interactions are repulsive, since attraction in specific channels are given by certain linear combinations of interaction parameters. On the other hand, pairing processes such as the exchange of spin fluctuations, are also present. We compare these two mechanisms on an equal footing using electronic bands appropriate for different classes of multiorbital systems over a wide range of interaction parame…
Multiorbital Hubbard models host strongly correlated 'Hund's metals' even for interactions much stronger than the bandwidth. We characterize this interaction-resilient metal as a mixed-valence state. In particular it can be pictured as a bridge between two strongly correlated insulators: a high-spin Mott insulator and a charge-disproportionated insulator which is stabilized by a very large Hund's coupling. This picture is confirmed comparing models with negative and positive Hund's coupling for different fillings. Our results provide a characterization of the Hund's metal state and connect its…
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…
We propose to combine the Trotter decomposition and a series expansion of the partition function for Hund's exchange coupling in a quantum Monte Carlo (QMC) algorithm for multiorbital systems that preserves spin and orbital rotational symmetries. This enables us to treat the Hund's (spin-flip and pair-hopping) terms, which is difficult in the conventional QMC method. To demonstrate this, we first apply the algorithm to study ferromagnetism in the two-orbital Hubbard model within the dynamical mean-field theory (DMFT). The result reveals that the preservation of the SU(2) symmetry in Hund's exc…
In order to resolve the long-standing issue of how the itinerant ferromagnetism is affected by the lattice structure and Hund's coupling, we have compared various three-dimensional lattice structures in the single- and multiorbital Hubbard models with the dynamical mean-field theory with an improved quantum Monte Carlo algorithm that preserves the spin-SU(2) symmetry. The result indicates that {\it both} the lattice structure and the d-orbital degeneracy are essential for the ferromagnetism in the parameter region representing a transition metal. Specifically, (a) Hund's coupling, despite the …
We develop an efficient approach for computing two-particle response functions and interaction vertices for multiorbital strongly correlated systems based on fluctuation around rotationally-invariant slave-boson saddle-point. The method is applied to the degenerate three-orbital Hubbard-Kanamori model for investigating the origin of the s-wave orbital antisymmetric spin-triplet superconductivity in the Hund's metal regime, previously found in the dynamical mean-field theory studies. By computing the pairing interaction considering the particle-particle and the particle-hole scattering channels…
We examine finite-temperature phase transitions in the two-orbital Hubbard model with different bandwidths by means of the dynamical mean-field theory combined with the continuous-time quantum Monte Carlo method. It is found that there emerges a peculiar slope-reversed first-order Mott transition between the orbital-selective Mott phase and the Mott insulator phase in the presence of Ising-type Hund's coupling. The origin of the slope-reversed phase transition is clarified by the analysis of the temperature dependence of the energy density. It turns out that the increase of Hund's coupling low…
We study the interplay of crystal field splitting and Hund coupling in a two-orbital model which captures the essential physics of systems with two electrons or holes in the e_g shell. We use single site dynamical mean field theory with a recently developed impurity solver which is able to access strong couplings and low temperatures. The fillings of the orbitals and the location of phase boundaries are computed as a function of Coulomb repulsion, exchange coupling and crystal field splitting. We find that the Hund coupling can drive the system into a novel Mott insulating phase with vanishing…
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…
Motivated by the relevance of Hund's coupling in the context of multiorbital superconductors, we revisit the problem of a multiorbital Kondo impurity with Hund's interaction. Using dynamical large-N techniques, we propose an efficient approach that retains the essential physics at play, while providing a pathway to scalable quantum impurity solvers. We are able to follow the ground state, dynamic, and thermodynamic properties of this system over many decades of temperature. Our approach captures the emergence of large moments, and follows the stretched evolution of the physics down to their ex…
We present a continuous-time Monte Carlo impurity solver for multiorbital impurity models which combines a strong-coupling hybridization expansion and a weak-coupling expansion in the Hund's coupling parameter J. This double-expansion approach allows to treat the dominant density-density interactions U within the efficient segment representation. We test the approach for a two-orbital model with static interactions, and then explain how the double-expansion allows to simulate models with frequency dependent U(ω) and J(ω). The method is used to investigate spin state transitions in a toy model …
Multiorbital systems such as the iron-based superconductors provide a new avenue to attack the longstanding problem of superconductivity in strongly correlated systems. In this work we study the superconductivity driven by a generic bosonic mechanism in a multiorbital model including the full dynamical electronic correlations induced by the Hubbard U and the Hund's coupling. We show that superconductivity survives much more in a Hund's metal than in an ordinary correlated metal with the same degree of correlation. The crucial role of the redistribution of spectral weight in the Hund's metal re…
Effect of rotationally-invariant Hund's rule coupling on a magnetism of multiorbital Hubbard models is studied within a dynamical mean field theory framework. Comparison of static magnetic susceptibilities and local densities of states of two- and three-orbital models of a complete rotationally invariant Coulomb interaction and a "density-density" Hartree type interaction shows the different role of spin-flip interactions for different band fillings. In the particle-hole symmetric case the Mott-Hubbard physics dominates due to the strong effective Coulomb interaction, while for the multiple el…
We investigate the violation of the first Hund's rule in 4$d$ and 5$d$ transition metal oxides that form solids of dimers. Bonding states within these dimers reduce the magnetization of such materials. We parametrize the dimer formation with realistic hopping parameters and find not only regimes, where the system behaves as a Fermi liquid or as a Peierls insulator, but also strongly correlated regions due to Hund's coupling and its competition with the dimer formation. The electronic structure is investigated using the cluster dynamical mean-field theory for a dimer in the two-plane Bethe latt…
We show the emergence of a new class of superconductivity in multiorbital systems, focusing on non-Kramers f$^2$ states. The Cooper pairs in this class of superconductivity mainly consist of local pairs with the same symmetry as the local f$^2$ ground states. When the local ground state is an anisotropic representation, the superconducting gap has nodes on the Fermi surface. This nodal superconductivity is mediated by the strong onsite inter-orbital attractions as a consequence of negative-$U$ physics generalized to multiorbital systems. We show that this is indeed realized in a simple two-orb…
We present a comprehensive study of a three-orbital lattice model suitable for the layered iridate Sr2IrO4. Our analysis includes various on-site interactions (including Hubbard and Hund's) as well as compressive strain, and a Zeeman magnetic field. We use a self-consistent mean field approach with multiple order parameters to characterize the resulting phases. While in some parameter regimes the compound is well described by an effective J=1/2 model, in other regimes the full multiorbital description is needed. As a function of the compressive strain, we uncover two quantum phase transitions:…
Superconductivity with a remarkably high $T_c$ has recently been found in Sr-doped NdNiO$_2$ thin films. While this system bears strong similarities to the cuprates, some differences, such as a weaker antiferromagnetic exchange coupling and possible high-spin moments on the doped Ni sites have been pointed out. Here, we investigate the effect of Hund coupling and crystal field splitting in a simple model system and argue that a multiorbital description of nickelate superconductors is warranted, especially in the strongly hole-doped regime. We then look at this system from the viewpoint of the …
The results of neutron scattering and angle-resolved photoemission experiments for the Fe-pnictide parent compounds, and their metallic nature, are shown to impose severe constraints on the range of values that can be considered "realistic" for the intraorbital Hubbard repulsion U and Hund coupling J in multiorbital Hubbard models treated in the mean-field approximation. Phase diagrams for three- and five-orbital models are here provided, and the physically realistic regime of couplings is highlighted, to guide future theoretical work into the proper region of parameters of Hubbard models. In …
We present a tree tensor-network impurity solver suited for general multiorbital systems. The network is constructed to efficiently capture the entanglement structure and symmetry of an impurity problem. The solver works directly on the real-time/frequency axis and generates spectral functions with energy-independent resolution of the order of one percent of the correlated bandwidth. Combined with an optimized representation of the impurity bath, it efficiently solves self-consistent dynamical mean-field equations and calculates various dynamical correlation functions for systems with off-diag…
Multiorbital systems away from global half-filling host intriguing physical properties promoted by Hund's coupling. Despite increasing awareness of this regime dubbed Hund's metal, effect of nonlocal interaction is still elusive. Here we study a three-orbital model with $1/3$ filling (two electrons per site) including the intersite Coulomb interaction ($V$). Using the $GW$ plus extended dynamical mean-field theory, the valence-skipping charge order transition is shown to be driven by $V$. Most interestingly, the instability to this transition is significantly enhanced in the spin-freezing cros…
We study spatial correlation effects in multiorbital systems, especially in a paramagnetic metallic state subject to Hund's coupling. We apply a cluster extension of the dynamical mean-field theory (DMFT) to the three-orbital Hubbard model away from half filling, where previous single-site DMFT studies revealed that local correlation effects caused by Hund's coupling bring about unusual strongly-correlated metallic behaviors. We find that Hund's coupling significantly affects the nonlocal correlations, too; it strongly modulates the electron distribution in the momentum space so as to make a m…
Theoretical studies recently predicted the condensation of spin-orbit excitons at momentum $q$=$π$ in $t_{2g}^4$ spin-orbit coupled three-orbital Hubbard models at electronic density $n=4$. In parallel, experiments involving iridates with non-integer valence states for the Ir ions are starting to attract considerable attention. In this publication, using the density matrix renormalization group technique we present evidence for the existence of a novel excitonic condensate at $n=3.5$ in a one-dimensional Hubbard model with a degenerate $t_{2g}$ sector, when in the presence of spin-orbit coupli…
We investigate superconducting pairing driven by electron-electron interactions in a theoretical model for monolayer MoS$_2$ with the temperature-flow functional renormalization group(fRG). At low doping, the dominant instability is toward odd-parity pairing with $f$-wave Mo-nearest-neighbor structure. We compute the fRG phase diagram versus electron doping below the van Hove filling of the conduction band. In the superconducting regime, the critical temperature grows with doping, comparable to the experiments. Near van Hove filling the system favors a ferromagnetic state. We demonstrate that …
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…
We studied a multi-orbital Hubbard model at half-filling for two and three orbitals per site on a two-site cluster via full exact diagonalization, in a wide range for the onsite repulsion $U$, from weak to strong coupling, and multiple ratios of the Hund coupling $J_H$ to $U$. The hopping matrix elements among the orbitals were also varied extensively. At intermediate and large $U$, we mapped the results into a Heisenberg model. For two orbitals per site, the mapping is into a $S=1$ Heisenberg model where by symmetry both nearest-neighbor $(\mathbf{S}_{i}\cdot\mathbf{S}_{j})$ and $(\mathbf{S}_…
A new class of high temperature superconductors based on iron and arsenic was recently discovered, with superconducting transition temperature as high as 55 K. Here we show, using microscopic theory, that the normal state of the iron pnictides at high temperatures is highly anomalous, displaying a Curie Weiss susceptibility and a linear temperature dependence of the resistivity. Below a coherence scale T*, the resistivity sharply drops and susceptibility crosses over to Pauli-like temperature dependence. Remarkably, the coherence-incoherence crossover temperature is a very strong function of t…
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…
To clarify the nature of correlations in Hund metals and its relationship with Mott physics we analyze the electronic correlations in multiorbital systems as a function of intraorbital interaction U, Hund's coupling JH and electronic filling n. We show that the main process behind the enhancement of correlations in Hund metals is the suppression of the double-occupancy of a given orbital, as it also happens in the Mott-insulator at half-filling. However, contrary to what happens in Mott correlated states the reduction of the quasiparticle weight Z with JH can happen on spite of increasing char…
Multiorbital interactions have the capacity to produce an interesting kind of doublon-holon bound state that consists of a single-hole state in one band and a doubly-occupied state in another band. Interband doublon-holon pair excitations in the two-orbital Hubbard model are studied by using dynamical mean-field theory with the Lanczos method as the impurity solver. We find that the interband bound states may provide several in-gap quasiparticle peaks in the density of states of the narrow band in the orbital-selective Mott phase with a small Hund's rule coupling ($J$). There exists a correspo…
An antiferromagnetic Hund coupling in multiorbital Hubbard systems induces orbital freezing and an associated superconducting instability, as well as unique composite orders in the case of an odd number of orbitals. While the rich phase diagram of the half-filled three-orbital model has recently been explored in detail, the properties of the doped system remain to be clarified. Here, we complement the previous studies by computing the entropy of the half-filled model, which exhibits an increase in the orbital-frozen region, and a suppression in the composite ordered phase. The doping dependent…
We analyze two different fermionic systems that defy Mott localization showing a metallic ground state at integer filling and very large Coulomb repulsion. The first is a multiorbital Hubbard model with a Hund's coupling, where this physics has been widely studied and the new metallic state is called a Hund's metal, and the second is a SU(3) Hubbard model with a patterned single-particle potential designed to display a similar interaction-resistant metal in a set-up which can be implemented with SU($N$) ultracold atoms. With simple analytical arguments and exact numerical diagonalization of th…
Hund's coupling in multiorbital systems allows for the possibility of even-parity orbital-antisymmetric spin-triplet pairing, which can be stabilized by spin-orbit coupling (SOC). While this pairing expressed in the orbital basis is uniform and spin-triplet, it appears in the band basis as a pseudospin-singlet, with the momentum dependence determined by the SOC and the underlying triplet character remaining in the form of interband pairing active away from the Fermi energy. Here, we examine the role of momentum-dependent SOC in generating nontrivial pairing symmetries, as well as the hidden tr…
A tight-band model is employed for the $e_{2g}$-orbitals in manganites. It is shown that a large intraatomic Hund's coupling, $J_H$ and the resulting double-exchange mechanism lead to antiferromagnetic ordering along one of the cubic axis stabilized by the cooperative JT effect which further decreases the band energy of electrons. As a result, LaMnO$_3$ is a band insulator built of 2D ferromagnetic layers. The critical concentration $x_c\simeq 0.16$, for onset of ferromagnetic and metallic behavior at low temperatures in La$_{1-x}$Sr$_x$MnO$_3$ and the phase transition are treated in the perco…
Hund metals have attracted attention in recent years due to their unconventional superconductivity, which supposedly originates from non-Fermi-liquid (NFL) properties of the normal state. When studying Hund metals using dynamical mean-field theory, one arrives at a self-consistent "Hund impurity problem" involving a multiorbital quantum impurity with nonzero Hund coupling interacting with a metallic bath. If its spin and orbital degrees of freedom are screened at different energy scales, $T_\mathrm{sp} < T_\mathrm{orb}$, the intermediate energy window is governed by a novel NFL fixed point, wh…
The alkali-doped fullerides A$_3$C$_{60}$ are half-filled three-orbital Hubbard systems which exhibit an unconventional superconducting phase next to a Mott insulator. While the pairing is understood to arise from an effectively negative Hund coupling, the highly unusual Jahn-Teller metal near the Mott transition, featuring both localized and itinerant electrons, has not been understood. This property is consistently explained by a previously unrecognized phenomenon: the spontaneous transition of multiorbital systems with negative Hund coupling into an orbital-selective Mott state. This symmet…
Using the Density Matrix Renormalization Group and two-leg ladders, we investigate an electronic two-orbital Hubbard model including plaquette diagonal hopping amplitudes. Our goal is to search for regimes where charges added to the undoped state form pairs, presumably a precursor of a superconducting state.For the electronic density $ρ=2$, i.e. the undoped limit, our investigations show a robust $(π,0)$ antiferromagnetic ground state, as in previous investigations. Doping away from $ρ=2$ and for large values of the Hund coupling $J$, a ferromagnetic region is found to be stable. Moreover, whe…
Hund's coupling assisted orbital-selective superconductivity in Ba1-xKxFe2As2
Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory（斯坦福材料能源科学研究所，SLAC国家加速器实验室）；Geballe Laboratory for Advanced Materials, Department of Applied Physics and Physics, Stanford University（斯坦福大学应用物理与物理系，Geballe先进材料实验室）；Department of Applied Physics, Stanford University（斯坦福大学应用物理系）；Department of Applied Physics, KTH-Royal Institute of Technology（瑞典皇家理工学院应用物理系）；National Institute of Advanced Industrial Science and Technology (AIST)（日本产业技术综合研究所）；Stanford Synchrotron Radiation Lightsource, SLAC National Accelerator Laboratory（SLAC国家加速器实验室斯坦福同步辐射光源）；Department of Material Science, Stanford University（斯坦福大学材料科学系）
Two-dimensional AKLT model on a honeycomb lattice has been shown to be a universal resource for quantum computation. In this valence bond solid, however, the spin interactions involve higher powers of the Heisenberg coupling $(\vec{S}_i \cdot \vec{S}_j)^n$, making these states seemingly unrealistic on bipartite lattices, where one expects a simple antiferromagnetic order. We show that those interactions can be generated by orbital physics in multiorbital Mott insulators. We focus on $t_{2g}$ electrons on the honeycomb lattice and propose a physical realization of the spin-$3/2$ AKLT state. We …
We study the interplay between the electron-electron (e-e) and the electron-phonon (e-ph) interactions in the two-orbital Hubbard-Holstein model at half filling using the dynamical mean field theory. We find that the e-ph interaction, even at weak couplings, strongly modifies the phase diagram of this model and introduces an orbital-selective Peierls insulating phase (OSPI) that is analogous to the widely studied orbital-selective Mott phase (OSMP). At small e-e and e-ph coupling, we find a competition between the OSMP and the OSPI, while at large couplings, a competition occurs between Mott a…
Survival of the metallic state in a single-hole multiband $p$-orbital molecular system
Osaka Metropolitan University（大阪公立大学）；University of California, Berkeley（加州大学伯克利分校）；National Institute of Standards and Technology (NIST)（美国国家标准与技术研究院）；Aristotle University of Thessaloniki（塞萨洛尼基亚里士多德大学）；Institute “Jožef Stefan”（约泽夫史丹福研究所）；Japan Synchrotron Radiation Research Institute (JASRI)（日本同步辐射研究机构）；RIKEN SPring-8 Center（理化学研究所SPring-8中心）；National Synchrotron Radiation Research Center（国家同步辐射研究中心）；Oak Ridge National Laboratory（橡树岭国家实验室）；University of Ljubljana（卢布尔雅那大学）
Motivated by the unexplored complexity of phases present in the multiorbital Hubbard model, we analyze in this work the behavior of a degenerate two-orbital anisotropic Hubbard model at half filling where both orbitals have equal bandwidths and one orbital is constrained to be paramagnetic (PM), while the second one is allowed to have an antiferromagnetic (AF) solution. Such a model may be relevant for a large class of correlated materials with competing magnetic states in different orbitals like the recently discovered Fe-based superconductors. Using a dynamical cluster approximation we obser…
We investigate the influence of spin-orbit coupling $λ$ in strongly-correlated multiorbital systems that we describe by a three-orbital Hubbard-Kanamori model on a Bethe lattice. We solve the problem at all integer fillings $N$ with the dynamical mean-field theory using the continuous-time hybridization expansion Monte Carlo solver. We investigate how the quasiparticle renormalization $Z$ varies with the strength of spin-orbit coupling. The behavior can be understood for all fillings except $N=2$ in terms of the atomic Hamiltonian (the atomic charge gap) and the polarization in the $j$-basis d…
Using the Density Matrix Renormalization Group technique we study the effect of spin-orbit coupling on a three-orbital Hubbard model in the $(t_{2g})^{4}$ sector and in one dimension. Fixing the Hund coupling to a robust value compatible with some multiorbital materials, we present the phase diagram varying the Hubbard $U$ and spin-orbit coupling $λ$, at zero temperature. Our results are shown to be qualitatively similar to those recently reported using the Dynamical Mean Field Theory in higher dimensions, providing a robust basis to approximate many-body techniques. Among many results, we obs…
The multiorbital Hubbard model in the strong coupling limit is analyzed for the effectively antiferromagnetic Hund's coupling relevant to fulleride superconductors with three orbitals per molecule. The localized spin-orbital model describes the thermodynamics of the half-filled (three-electron) state with total spin-1/2, composed of singlon and doublon placed on the two of three orbitals. The model is solved using the mean-field approximation and magnetic and electric ordered states are clarified through the temperature dependences of the order parameters. Combining the model with the band str…
We report a Fe Kβx-ray emission spectroscopy study of local magnetic moments in the rare-earth doped iron pnictide Ca_{1-x}RE_xFe_2As_2 (RE=La, Pr, and Nd). In all samples studied the size of the Fe local moment is found to decrease significantly with temperature and goes from ~0.9 μ_B at T = 300 K to ~0.45 μ_B at T = 70 K. In the collapsed tetragonal (cT) phase of Nd- and Pr-doped samples (T<70K) the local moment is quenched, while the moment remains unchanged for the La-doped sample, which does not show lattice collapse. Our results show that Ca_{1-x}RE_xFe_2As_2 (RE= Pr and Nd) exhibits a s…
