Multiorbital Hubbard Model Research Articles

Description of molecular nanomagnets by the multiorbital Hubbard model with correlated hopping

We present a microscopic description of molecular magnets by the multiorbital Hubbard model, which includes the correlated hopping term, i.e., the dependence of the electron hopping amplitude between orbitals on the degree of their occupancy. In the limit of large Coulomb on-site interaction, we derive the spin Hamiltonian using the perturbation theory. We determine the magnetic coupling constant between two ions in two different ways: (a) from the expression obtained in the perturbation calculus and (b) from the analysis of distances between the lowest levels of the energy spectrum obtained by diagonalization of the multiorbital Hubbard model. The procedure we use can be applied to various nanomagnets, but we perform the final calculations for the molecular ring ${\text{Cr}}_{8}$. We show that the correlated hopping can reduce the antiferromagnetic exchange between ions, which is essential for a proper description of ${\mathrm{Cr}}_{8}$.

Spin-orbital model for fullerides

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 structure from {\it ab initio} calculation, we also semi-quantitavely analyze the realistic model and the corresponding physical quantities. In the A15-structure fulleride model, there is an antiferromagnetic ordered state, and subsequently the two orbital ordered state appears at lower temperatures. It is argued that the origin of these orbital orders is related to the $T_h$ point group symmetry. As for the fcc-fulleride model, the time-reversal broken orbital ordered state is identified. Whereas the spin degeneracy remains in our treatment for the geometrically frustrated lattice, it is expected to be lifted by some magnetic ordering or quantum fluctuations, but not by the spin-orbital coupling which is effectively zero for fullerides in the strong-coupling regime.

Interaction-resistant metals in multicomponent Fermi systems

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 (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 setup which can be implemented with $\mathrm{SU}(N)$ ultracold atoms. With simple analytical arguments and exact numerical diagonalization of the Hamiltonians for a minimal three-site system, we demonstrate that the interaction-resistant metal emerges in both cases as a compromise between two different insulating solutions which are stabilized by different terms of the models. This provides strong evidence that the Hund's metal is a specific realization of a more general phenomenon which can be realized in various strongly correlated systems.

Orbital-selective coherence-incoherence crossover and metal-insulator transition in Cu-doped NaFeAs

We study the effects of electron-electron interactions and hole doping on the electronic structure of Cu-doped NaFeAs using the density functional theory plus dynamical mean-field theory (DFT+DMFT) method. In particular, we employ an effective multi-orbital Hubbard model with a realistic bandstructure of NaFeAs in which Cu-doping was modeled within a rigid band approximation and compute the evolution of the spectral properties, orbital-dependent electronic mass renormalizations, and magnetic properties of NaFeAs upon doping with Cu. In addition, we perform fully charge self-consistent DFT+DMFT calculations for the long-range antiferromagnetically ordered Na(Fe,Cu)As with Cu $x=0.5$ with a real-space ordering of Fe and Cu ions. Our results reveal a crucial importance of strong electron-electron correlations and local potential difference between the Cu and Fe ions for understanding the \textbf{k}-resolved spectra of Na(Fe,Cu)As. Upon Cu-doping, we observe a strong orbital-dependent localization of the Fe $3d$ states accompanied by a large renormalization of the Fe $xy$ and $xz$/$yz$ orbitals. Na(Fe,Cu)As exhibits bad metal behavior associated with a coherence-to-incoherence crossover of the Fe $3d$ electronic states and local moments formation near a Mott metal-insulator transition (MIT). For heavily doped NaFeAs with Cu $x \sim 0.5$ we obtain a Mott insulator with a band gap of $\sim$0.3 eV characterized by divergence of the quasiparticle effective mass of the Fe $xy$ states. In contrast to this, the quasiparticle weights of the Fe $xz$/$yz$ and $e_g$ states remain finite at the MIT. The MIT occurs via an orbital-selective Mott phase to appear at Cu $x\simeq0.375$ with the Fe $xy$ states being Mott localized. We propose the possible importance of Fe/Cu disorder to explain the magnetic properties of Cu-doped NaFeAs.

Orbital ordering in the layered perovskite material CsVF4

In strongly correlated electronic systems, several novel physical properties are induced by the orbital degree of freedom. In particular, orbital degeneracy near the Fermi level leads to spontaneous symmetry breaking, such as the nematic state in FeSe and the orbital ordering in several perovskite systems. Here, the novel layered perovskite material CsVF$_4$, with a $3d^2$ electronic configuration, was systematically studied using density functional theory and a multiorbital Hubbard model within the Hatree-Fock approximation. Our results show that CsVF$_4$ should be magnetic, with a G-type antiferromagnetic arrangement in the $ab$ plane and weak antiferromagnetic exchange along the $c$-axis, in agreement with experimental results. Driven by the Jahn-Teller distortion in the VF$_6$ octahedra that shorten the $c$-axis, the system displays an interesting electron occupancy $d_{xy}^1(d_{xz}d_{yz})^1$ corresponding to the lower nondegenerate $d_{xy}$ orbital being half-filled and the other two degenerate $d_{yz}$ and $d_{xz}$ orbitals sharing one electron per site. We show that this degeneracy is broken and a novel $d_{yz}$/$d_{xz}$ staggered orbital pattern is here predicted by both the first-principles and Hubbard model calculations. This orbital ordering is driven by the electronic instability associated with degeneracy removal to lower the energy.

Enhancement of charge instabilities in Hund's metals by breaking of rotational symmetry

We analyze multi-orbital Hubbard models describing Hund's metals, focusing on the ubiquitous occurrence of a charge instability, signalled by a divergent/negative electronic compressibility, in a range of doping from the half-filled Mott insulator corresponding to the frontier between Hund's and normal metals. We show that the breaking of rotational invariance favors this instability: both spin-anisotropy in the interaction and crystal-field splitting among the orbitals make the instability zone extend to larger dopings, making it relevant for real materials like iron-based superconductors. These observations help us build a coherent picture of the occurrence and extent of this instability. We trace it back to the partial freezing of the local degrees of freedom in the Hund's metal, which reduces the allowed local configurations and thus the quasiparticle itinerancy. The abruptness of the unfreezing happening at the Hund's metal frontier can be directly connected to a rapid change in the electronic kinetic energy and thus to the enhancement and divergence of the compressibility.

Disordered Mott-Hubbard Physics in Nanoparticle Solids: Transitions Driven by Disorder, Interactions, and Their Interplay.

We show that adapting the knowledge developed for the disordered Mott-Hubbard model to nanoparticle (NP) solids can deliver many very helpful new insights. We developed a hierarchical nanoparticle transport simulator (HINTS), which builds from localized states to describe the disorder-localized and Mott-localized phases of NP solids and the transitions out of these localized phases. We also studied the interplay between correlations and disorder in the corresponding multiorbital Hubbard model at and away from integer filling by dynamical mean field theory. This DMFT approach is complementary to HINTS, as it builds from the metallic phase of the NP solid. The mobility scenarios produced by the two methods are strikingly similar and account for the mobilities measured in NP solids. We conclude this work by constructing the comprehensive phase diagram of PbSe NP solids on the disorder-filling plane.

Block orbital-selective Mott insulators: A spin excitation analysis

We present a comprehensive study of the spin excitations - as measured by the dynamical spin structure factor $S(q,\omega)$ - of the so-called block-magnetic state of low-dimensional orbital-selective Mott insulators. We realize this state via both a multi-orbital Hubbard model and a generalized Kondo-Heisenberg Hamiltonian. Due to various competing energy scales present in the models, the system develops periodic ferromagnetic islands of various shapes and sizes, which are antiferromagnetically coupled. The 2$\times$2 particular case was already found experimentally in the ladder material BaFe$_2$Se$_3$ that becomes superconducting under pressure. Here we discuss the electronic density as well as Hubbard and Hund coupling dependence of $S(q,\omega)$ using density matrix renormalization group method. Several interesting features were identified: (1) An acoustic (dispersive spin-wave) mode develops. (2) The spin-wave bandwidth establishes a new energy scale that is strongly dependent on the size of the magnetic island and becomes abnormally small for large clusters. (3) Optical (dispersionless spin excitation) modes are present for all block states studied here. In addition, a variety of phenomenological spin Hamiltonians have been investigated but none matches entirely our results that were obtained primarily at intermediate Hubbard $U$ strengths. Our comprehensive analysis provides theoretical guidance and motivation to crystal growers to search for appropriate candidate materials to realize the block states, and to neutron scattering experimentalists to confirm the exotic dynamical magnetic properties unveiled here, with a rich mixture of acoustic and optical features.

Tightening the Lieb-Robinson Bound in Locally Interacting Systems

The Lieb-Robinson (LR) bound rigorously shows that in quantum systems with short-range interactions, the maximum amount of information that travels beyond an effective "light cone" decays exponentially with distance from the light-cone front, which expands at finite velocity. Despite being a fundamental result, existing bounds are often extremely loose, limiting their applications. We introduce a method that dramatically and qualitatively improves LR bounds in models with finite-range interactions. Most prominently, in systems with a large local Hilbert space dimension $D$, our method gives an LR velocity that grows much slower than previous bounds with $D$ as $D\to \infty$. For example, in the Heisenberg model with spin $S$, we find $v\leq$ const. compared to the previous $v\propto S$ which diverges at large $S$, and in multiorbital Hubbard models with $N$ orbitals, we find $v\propto \sqrt{N}$ instead of previous $v\propto N$, and similarly in the $N$-state truncated Bose-Hubbard model and Wen's quantum rotor model. Our bounds also scale qualitatively better in some systems when the spatial dimension or certain model parameters become large, for example in the $d$-dimensional quantum Ising model and perturbed toric code models. Even in spin-1/2 Ising and Fermi-Hubbard models, our method improves the LR velocity by an order of magnitude with typical model parameters, and significantly improves the LR bound at large distance and early time.

Superconducting mechanism for the cuprate Ba2CuO3+δ based on a multiorbital Lieb lattice model

For the recently discovered cuprate superconductor $\mathrm{Ba_{2}CuO_{3+\delta}}$, we propose a lattice structure which resembles the model considered by Lieb to represent the vastly oxygen-deficient material. We first investigate the stability of the Lieb-lattice structure, and then construct a multiorbital Hubbard model based on first-principles calculation. By applying the fluctuation-exchange approximation to the model and solving the linearized Eliashberg equation, we show that $s$-wave and $d$-wave pairings closely compete with each other, and, more interestingly, that the intra-orbital and inter-orbital pairings coexist. We further show that, if the energy of the $d_{3z^2-r^2}$ band is raised to make it "incipient" with the lower edge of the band close to the Fermi level within a realistic band filling regime, $s\pm$-wave superconductivity is strongly enhanced. We reveal an intriguing relation between the Lieb model and the two-orbital model for the usual K$_2$NiF$_4$ structure where a close competition between $s-$ and $d-$wave pairings is known to occur. The enhanced superconductivity in the present model is further shown to be related to an enhancement found previously in the bilayer Hubbard model with an incipient band.

Anisotropic superexchange through nonmagnetic anions with spin-orbit coupling

Anisotropic superexchange interaction is one of the most important interactions in realizing exotic quantum magnetism, which is traditionally regarded to originate from magnetic ions and has no relation with the nonmagnetic ions. In our work, by studying a multi-orbital Hubbard model with spin-orbit coupling on both magnetic cations and nonmagnetic anions, we analytically demonstrate that the spin-orbit coupling on nonmagnetic anions alone can induce antisymmetric Dzyaloshinskii-Moriya interaction, symmetric anisotropic exchange and single ion anisotropy on the magnetic ions and thus it actually contributes to anisotropic superexchange on an equal footing as that of magnetic ions. Our results promise one more route to realize versatile exotic phases in condensed matter systems, long-range orders in low dimensional materials and switchable single molecule magnetic devices for recording and manipulating quantum information through nonmagnetic anions.

Dzyaloshinskii–Moriya Interaction between Multipolar Moments in 5d1 Systems

We propose a new type of Dzyaloshinskii-Moriya (DM) interactions which act on high-rank multipolar moments such as quadrupolar and octupolar moments. Here we consider 5d1 systems with broken spatial inversion symmetry, where the interplay of electron correlation, the spin-orbit coupling, and inversion symmetry breaking plays a crucial role. Using a numerical diagonalization on a two-site multiorbital Hubbard model, we reveal that anti-symmetric products of multipole operators have finite expectation values, indicating the existence of DM interactions for multipoles. We also find that the spin-orbit coupling dependences of DM interactions for multipoles are significantly different depending on the lattice structure. Finally, we discuss the numerical results for small and large spin-orbit coupling region by using perturbative analysis.

Structural, electrical, magnetic, and optical properties of iron-based ladder compounds BaFe2(S1−xSex)3

We performed a comprehensive study on structural, electrical, magnetic, and optical properties for iron-based ladder materials ${\mathrm{BaFe}}_{2}{({\mathrm{S}}_{1\ensuremath{-}x}{\mathrm{Se}}_{x})}_{3}\phantom{\rule{4pt}{0ex}}(0\ensuremath{\le}x\ensuremath{\le}1)$, which shows pressure-induced superconductivity in the vicinity of the Mott transition at $x=0$ and 1. We obtain a complete electronic phase diagram in a temperature-composition plane, which reveals that the magnetic ground state switches from the stripe-type to the block-type phase without any intermediate phase at $x=0.23$ with increasing $x$. This behavior is in sharp contrast to the filling controlled system ${\mathrm{Ba}}_{1\ensuremath{-}x}\phantom{\rule{4pt}{0ex}}{\mathrm{Cs}}_{x}{\mathrm{Fe}}_{2}{\mathrm{Se}}_{3}$, in which a paramagnetic state down to the lowest temperature is realized between two magnetic ordered states. The structural transition, which is considered to be relevant to the orbital order, occurs far above the magnetic transition temperature. The magnetic and structural transition temperatures exhibit a similar composition dependence, indicating a close relationship between magnetic and orbital degrees of freedom. In addition, we found that charge dynamics are considerably influenced not only by the magnetic order but also by the structural change (orbital order) from the detailed measurements of electrical resistivity and optical conductivity spectra. We discuss the magnetism and orbital order by comparing the experimental results with the proposed theory based on the multiorbital Hubbard model. The relationship between the charge dynamics and the magnetic/orbital order is also discussed.

Block–spiral magnetism: An exotic type of frustrated order

Competing interactions in quantum materials induce exotic states of matter such as frustrated magnets, an extensive field of research from both the theoretical and experimental perspectives. Here, we show that competing energy scales present in the low-dimensional orbital-selective Mott phase (OSMP) induce an exotic magnetic order, never reported before. Earlier neutron-scattering experiments on iron-based 123 ladder materials, where OSMP is relevant, already confirmed our previous theoretical prediction of block magnetism (magnetic order of the form [Formula: see text]). Now we argue that another phase can be stabilized in multiorbital Hubbard models, the block-spiral state. In this state, the magnetic islands form a spiral propagating through the chain but with the blocks maintaining their identity, namely rigidly rotating. The block-spiral state is stabilized without any apparent frustration, the common avenue to generate spiral arrangements in multiferroics. By examining the behavior of the electronic degrees of freedom, parity-breaking quasiparticles are revealed. Finally, a simple phenomenological model that accurately captures the macroscopic spin spiral arrangement is also introduced, and fingerprints for the neutron-scattering experimental detection are provided.

Signatures of bosonic excitations in high-harmonic spectra of Mott insulators

The high harmonic spectrum of the Mott insulating Hubbard model has recently been shown to exhibit plateau structures with cutoff energies determined by $n$th nearest neighbor doublon-holon recombination processes. The spectrum thus allows to extract the on-site repulsion $U$. Here, we consider generalizations of the single-band Hubbard model and discuss the signatures of bosonic excitations in high harmonic spectra. Specifically, we study an electron-plasmon model which captures the essential aspects of the dynamically screened Coulomb interaction in solids and a multi-orbital Hubbard model with Hund coupling which allows to analyze the effect of local spin excitations. For the electron-plasmon model, we show that the high harmonic spectrum can reveal information about the screened and bare onsite interaction, the boson frequency, as well as the relation between boson coupling strength and boson frequency. In the multi-orbital case, string states formed by local spin excitations result in an increase of the radiation intensity and cutoff energy associated with higher order recombination processes.

Alleviating the sign problem in quantum Monte Carlo simulations of spin-orbit-coupled multiorbital Hubbard models

We present a strategy to alleviate the sign problem in continuous-time quantum Monte Carlo (CTQMC) simulations of the dynamical-mean-field-theory (DMFT) equations for the spin-orbit-coupled multiorbital Hubbard model. We first identify the combinations of rotationally invariant Hund coupling terms present in the relativistic basis which lead to a severe sign problem. Exploiting the fact that the average sign in CTQMC depends on the choice of single-particle basis, we propose a bonding-antibonding basis $V_{j3/2\mathrm{BA}}$ which shows an improved average sign compared to the widely used relativistic basis for most parameter sets investigated. We then generalize this procedure by introducing a stochastic optimization algorithm that exploits the space of single-particle bases and show that $V_{j3/2\mathrm{BA}}$ is very close to optimal within the parameter space investigated. Our findings enable more efficient DMFT simulations of materials with strong spin-orbit coupling.

Effect of Nonlocal Correlations on the Electronic Structure of LiFeAs.

We investigate the role of nonlocal correlations in LiFeAs by exploring an abinitio-derived multiorbital Hubbard model for LiFeAs via the two-particle self-consistent (TPSC) approach. The multiorbital formulation of TPSC approximates the irreducible interaction vertex to be an orbital-dependent constant, which is self-consistently determined from local spin and charge sum rules. Within this approach, we disentangle the contribution of local and nonlocal correlations in LiFeAs and show that in the local approximation one recovers the dynamical mean field theory result. The comparison of our theoretical results to most recent angular-resolved photoemission spectroscopy and de Haas-van Alphen data shows that nonlocal correlations in LiFeAs are decisive to describe the measured spectral function A(k[over →],ω), Fermi surface, and scattering rates. These findings underline the importance of nonlocal correlations and benchmark different theoretical approaches for iron-based superconductors.

Doping-driven metal-insulator transition in correlated electron systems with strong Hund's exchange coupling

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 transition, a regime with frozen local moments develops only on the branch connected to the insulating phase.

Large effect of metal substrate on magnetic anisotropy of Co on hexagonal boron nitride

We combine x-ray absorption spectroscopy (XAS), x-ray magnetic circular dichroism (XMCD) and x-ray magnetic linear dichroism (XMLD) data with first principles density functional theory (DFT) calculations and a multiorbital many-body Hamiltonian approach to understand the electronic and magnetic properties of Co atoms adsorbed on h-BN/Ru(0001) and h-BN/Ir(111). The XAS line shape reveals, for both substrates, an electronic configuration close to 3d8, corresponding to a spin S = 1. Magnetic field dependent XMCD data show large (14 meV) out-of-plane anisotropy on h-BN/Ru(0001), while it is almost isotropic (tens of μeV) on h-BN/Ir(111). XMLD data together with both DFT calculations and the results of the multiorbital Hubbard model suggest that the dissimilar magnetic anisotropy originates from different Co adsorption sites, namely atop N on h-BN/Ru(0001) and 6-fold hollow on h-BN/Ir(111).

Charge Disproportionation, Mixed Valence, and Janus Effect in Multiorbital Systems: A Tale of Two Insulators.

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 presence with charge disproportionation, which has indeed been observed in chromates and proposed to play a role in iron-based superconductors.