We introduce a variational state for one-dimensional two-orbital Hubbard models that intuitively explains the recent computational discovery of pairing in these systems when hole doped. Our Ansatz is an optimized linear superposition of Affleck-Kennedy-Lieb-Tasaki valence bond states, rendering the combination a valence bond liquid dubbed Orbital Resonant Valence Bond. We show that the undoped (one electron/orbital) quantum state of two sites coupled into a global spin singlet is exactly written employing only spin-1/2 singlets linking orbitals at nearest-neighbor sites. Generalizing to longer chains defines our variational state visualized geometrically expressing our chain as a two-leg ladder, with one orbital per leg. As in Anderson's resonating valence-bond state, our undoped variational state contains preformed singlet pairs that via doping become mobile leading to superconductivity. Doped real materials with one-dimensional substructures, two near-degenerate orbitals, and intermediate Hubbard U/W strengths -- W the carrier's bandwidth -- could realize spin-singlet pairing if on-site anisotropies are small. If these anisotropies are robust, spin-triplet pairing emerges.
In the framework of a multiorbital Hubbard model description of superconductivity, a matrix formulation of the superconducting pairing interaction that has been widely used is designed to treat spin, charge and orbital fluctuations within a random phase approximation (RPA). In terms of Feynman diagrams, this takes into account particle-hole ladder and bubble contributions as expected. It turns out, however, that this matrix formulation also generates additional terms which have the diagrammatic structure of vertex corrections. Here we examine these terms and discuss the relationship between th…
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 …
To understand the recently established unique magnetic and superconducting phase diagram of LaFeAsO$_{1-x}$H$_x$, we analyze the realistic multiorbital tight-binding model for $x=0 \sim 0.4$ beyond the rigid band approximation. Both the spin and orbital susceptibilities are calculated in the presence of the Coulomb and charge quadrupole interactions. It is found that both orbital and spin fluctuations strongly develop at both $x \sim 0$ and 0.4, due to the strong violation of the rigid band picture in LaFeAsO$_{1-x}$H$_x$. Based on this result, we discuss the experimental phase diagram, especi…
Multi-orbital Hubbard model Hamiltonians for the undoped parent compounds of the Fe-pnictide superconductors are here investigated using mean-field techniques. For a realistic four-orbital model, our results show the existence of an intermediate Hubbard U coupling regime where the mean-field ground state has spin stripe magnetic order, as in neutron scattering experiments, while remaining metallic, due to the phenomenon of band overlaps. The angle-resolved photoemission intensity and Fermi surface of this magnetic and metallic state are discussed. Other models are also investigated, including …
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 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 study the two band degenerate Hubbard model using the Fluctuation Exchange approximation (FLEX) method and compare the results with Quantum Monte-Carlo calculations. Both the self-consistent and the non-self-consistent versions of the FLEX scheme are investigated. We find that, contrary to the one band case, in the multiband case, good agreement with the Quantum Monte-Carlo results is obtained within the electron-electron T-matrix approximation using the full renormalization of the one-particle propagators. The crossover to strong coupling and the formation of satellites is more clearly vis…
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 …
By means of dynamical mean-field theory allowing for complete account of SU(2) rotational symmetry of interactions between spin-1/2 particles, we observe a strong effect of suppression of ferromagnetic order in the multiorbital Fermi-Hubbard model in comparison with a widely used restriction to density-density interactions. In the case of orbital degeneracy, we show that the suppression effect is the strongest in the two-orbital model (with effective spin $S_{\rm eff}=1$) and significantly decreases when considering three orbitals ($S_{\rm eff}=3/2$), thus magnetic ordering can effectively rev…
Recent experiments on Zn-doped 122-type iron pnictides, Ba(Fe$_{1-x-y}$Co$_y$Zn$_x$)$_2$As$_2$, are challenging our understanding of electron doping the 122s and the interplay between doping and impurity scattering. To resolve this enigma, we investigate the disorder effects of nonmagnetic Zn impurities in the strong (unitary) scattering limit on various properties of the system in the $s_{\pm}$-wave superconducting pairing state. The lattice Bogoliubov-de Gennes equation (BdG) is solved self-consistently based on a minimal two-orbital model with an extended range of impurity concentrations. W…
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…
Temperature dependence of thermopower in the multiorbital Hubbard model is studied by using the dynamical mean-field theory with the non-crossing approximation impurity solver. It is found that the Coulomb interaction, the Hund coupling, and the crystal filed splitting bring about non-monotonic temperature dependence of the thermopower, including its sign reversal. The implication of our theoretical results to some materials is discussed.
The role of the multiorbital effects on the emergence of frustrated electronic orders on the triangular lattice at half filling is investigated through an extended spinless fermion Hubbard model. By using two complementary approaches, unrestricted Hartree-Fock and exact diagonalizations, we unravel a very rich phase diagram controlled by the strength of both local and off-site Coulomb interactions and by the interorbital hopping anisotropy ratio $t'/t$. Three robust unconventional electronic phases, a pinball liquid, an inverse pinball liquid, and a large-unit-cell $\sqrt{12} \times \sqrt{12}$…
The orbital-selective Mott phase (OSMP) of multiorbital Hubbard models has been extensively analyzed before using static and dynamical mean-field approximations. In parallel, the properties of Block states (antiferromagnetically coupled ferromagnetic spin clusters) in Fe-based superconductors have also been much discussed. The present effort uses numerically exact techniques in one-dimensional systems to report the observation of Block states within the OSMP regime, connecting two seemingly independent areas of research, and providing analogies with the physics of Double-Exchange models.
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}_…
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…
There is increasing recognition that the multiorbital nature of the 3d electrons is important to the proper description of the electronic states in the normal state of the iron-based superconductors. Earlier studies of the pertinent multiorbital Hubbard models identified an orbital-selective Mott phase, which anchors the orbital-selective behavior seen in the overall phase diagram. An important characteristics of the models is that the orbitals are kinetically coupled -- i.e. hybridized -- to each other, which makes the orbital-selective Mott phase especially nontrivial. A U(1) slave-spin meth…
In order to discuss the spin-gap formation in a multiorbital system, we analyze an e_g-orbital Hubbard model on a geometrically frustrated zigzag chain by using a density-matrix renormalization group method. Due to the appearance of a ferro-orbital arrangement, the system is regarded as a one-orbital system, while the degree of spin frustration is controlled by the spatial anisotropy of the orbital. In the region of strong spin frustration, we observe a finite energy gap between ground and first-excited states, which should be called a spin-orbital gap. The physical meaning is clarified by an …
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…
Experiments on polarized fermion gases performed by trapping ultracold atoms in optical lattices, allow the study of an attractive Hubbard model for which the strength of the on site interaction is tuned by means of a Feshbach resonance. Using a well-known particle-hole transformation we discuss how results obtained for this system can be reinterpreted in the context of a doped repulsive Hubbard model. In particular we show that the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state corresponds to the striped state of the two-dimensional doped positive U Hubbard model. We then use the results of nu…
We calculate the charge compressibility and uniform spin susceptibility for the two-dimensional (2D) Hubbard model slightly away from half-filling within a two-loop renormalization group scheme. We find numerically that both those quantities flow to zero as we increase the initial interaction strength from weak to intermediate couplings. This result implies gap openings in both charge and spin excitation spectra for the latter interaction regime. When this occurs, the ground state of the lightly doped 2D Hubbard model may be interpreted as an insulating spin liquid as opposed to a Mott insulat…
Motivated by the nematic electronic fluid phase in Sr_{3}Ru_{2}O_{7}, we develop a combined scheme of the renormalization-group method and the random-phase-approximation-type method, and analyze orbital susceptibilities of the (d_{xz},d_{yz})-orbital Hubbard model with high accuracy. It is confirmed that the present model exhibits a ferro-orbital instability near the magnetic or superconducting quantum criticality, due to the Aslamazov-Larkin-type vertex corrections. This mechanism of orbital nematic order presents a natural explanation for the nematic order in Sr_{3}Ru_{2}O_{7}, and is expect…
Doped Hubbard model is a simple model for the high-Tc cuprate superconductors, while its ground state remains a challenge. Here, by performing state-of-the-art variational Monte Carlo calculations for the strong-coupling Hubbard model, we find evidences that the d-wave superconducting phase emerges always near the phase separation region and the superconducting order has one-to-one correspondence with the enhancement of charge compressibility. The order as well as the phase separation are vulnerable to realistic intersite Coulomb interaction while the superexchange interaction enhances both. A…
We study the thermally driven spin state transition in a two-orbital Hubbard model with crystal field splitting, which provides a minimal description of the physics of LaCoO3. We employ the dynamical mean-field theory with quantum Monte-Carlo impurity solver. At intermediate temperatures we find a spin disproportionated phase characterized by checkerboard order of sites with small and large spin moments. The high temperature transition from the disproportionated to a homogeneous phase is accompanied by vanishing of the charge gap. With the increasing crystal-field splitting the temperature ran…
We study the ground state properties of the doped Hubbard model with strong interactions on honeycomb lattice by the Density Matrix Renormalization Group (DMRG) method. At half-filling, due to the absence of minus sign problem, it is now well established by large-scale Quantum Monte Carlo calculations that a Dirac semi-metal to anti-ferromagnetic Mott insulator transition occurs with the increase of the interaction strength $U$ for the Hubbard model on honeycomb lattice. However, an understanding of the fate of the anti-ferromagnetic Mott insulator when holes are doped into the system is still…
Superconductivity enhancement and particle-hole asymmetry: interplay with electron attraction in doped Hubbard model
School of Physical Science and Technology, ShanghaiTech University（上海科技大学理学院）；Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory and Stanford University（斯坦福大学材料能源科学研究所、SLAC国家加速器实验室和斯坦福大学）
To clarify a key role of orbital degrees of freedom in the response of the many-body electron state of correlated electrons to an external field, we investigate the real-time dynamics in an $e_{\rm g}$-orbital Hubbard model under applied electric fields by exploiting numerical techniques such as a time-dependent density-matrix renormalization group (DMRG) method. The ground state without applying an electric field is found to be an antiferromagnetic/ferro-orbital state. After we switch on an oscillating electric field, it gives rise to the creation of holon-doublon pairs when the frequency of …
We present determinant quantum Monte Carlo simulations of the hole-doped single-band Hubbard-Holstein model on a square lattice, to investigate how quasiparticles emerge when doping a Mott insulator (MI) or a Peierls insulator (PI). The MI regime at large Hubbard interaction $U$ and small relative electron-phonon coupling strength $λ$ is quickly suppressed upon doping, by drawing spectral weight from the upper Hubbard band and shifting the lower Hubbard band towards the Fermi level, leading to a metallic state with emergent quasiparticles at the Fermi level. On the other hand, the PI regime at…
Orbital polarization and electronic correlation are two essential aspects in understanding the normal state and superconducting properties of multiorbital FeAs-based superconductors. In this Letter, we present a systematical study on the orbital polarization of iron pnictides from weak to strong Coulomb correlations within the KRSB approach. The magnetic phase diagram of the two-orbital model for LaFeAsO clearly shows that the striped antiferromagnetic metallic phase with considerable orbital polarization exists over a wide doping range. The reversal of the orbital polarization occurs in the i…
The natural orbitals renormalization group (NORG) has previously been proposed as an efficient numerical method for solving zero-temperature properties of multisite and multiorbital quantum impurity systems. Here, we implement the NORG as an impurity solver for dynamical mean-field theory (DMFT). In comparison with the exact diagonalization method, the NORG method can treat much more bath sites in an impurity model to which the DMFT maps a lattice model and can find accurate zero-temperature Matsubara and low-frequency retarded Green's functions. We demonstrate the effectiveness of this method…
We present theoretical analysis of Hall effect in doped Mott-Hubbard insulator, considered as a prototype of cuprate superconductor. We consider the standard Hubbard model within DMFT approximation. As a typical case we consider the partially filled (hole doping) lower Hubbard band. We calculate the doping dependence of both the Hall coefficient and Hall number and determine the value of carrier concentration, where Hall effect changes its sign. We obtain a significant dependence of Hall effect parameters on temperature. Disorder effects are taken into account in a qualitative way.We also perf…
By making use of the self-consistent projection operator method with high-momentum and high-energy resolutions, we find a kink structure in the quasiparticle excitation spectrum of the two-dimensional Hubbard model in the underdoped regime. The kink is caused by a mixing between the quasiparticle state and excitations with short-range antiferromagnetic order. We suggest that this might be the origin of the strong concentration dependence of the 'kink' found in La_{2-x}Sr_{x}CuO_{4} (x=0.03-0.07).
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 the weak coupling limit, we investigate two-leg ladders with a unit cell containing both Cu and O atoms, as a function of doping. For purely repulsive interactions, using bosonization, we find significant differences with the single orbital case: a completely massless quantum critical regime is obtained for a finite range of carrier concentration. In a broad region of the phase diagram the ground state consists of a pattern of orbital currents plus a density wave. NMR properties of the Cu and O nuclei are presented for the various phases.
Within the Kotliar-Ruckenstein slave-boson approach, we have studied the antiferromagnetic (AF) properties for the $t$-$t'$-$t''$-$U$ model applied to electron-doped cuprate superconductors. Due to inclusion of spin fluctuations the AF order decreases with doping much faster than obtained in the Hartree-Fock theory. Under an intermediate {\it constant} $U$ the calculated doping evolution of the spectral intensity has satisfactorily reproduced the experimental results, without need of a strongly doping-dependent $U$ as argued earlier. This may reconcile a discrepancy suggested in recent studies…
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…
In order to numerically study electron correlation effects in multi-orbital systems, we propose a new type of discrete transformation for the exchange (Hund's coupling) and pair-hopping interactions to be used in the dynamical mean field theory + quantum Monte Carlo method. The transformation, which is real and exact, turns out to suppress the sign problem in a wide parameter region including non-half-filled bands. This enables us to obtain the dominant pairing symmetry in the double-orbital Hubbard model, which shows that the spin-triplet, orbital-antisymmetric pairing that exploits Hund's co…
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…
Motivated by the recent resurgence of interest in topological superconductivity, we study in this paper superconducting pairing instabilities of the hole-doped Rashba-Hubbard model on the square lattice with first- and second-neighbor hopping. Within a weak-coupling approach based on the random phase approximation, we compute the spin-fluctuation mediated paring interactions as a function of spin-orbit coupling and hole doping. Rashba spin-orbit coupling splits the spin degeneracies of the bands, which leads to two van Hove singularities at two different fillings. We find that for a broad dopi…
We study by the Gutzwiller approximation the melting of the valence bond crystal phase of a bilayer Hubbard model at sufficiently large inter-layer hopping. We find that a superconducting domain, with order parameter $d_{z^2-r^2}$, $z$ being the inter-layer direction and $r$ the intra-layer one, is stabilized variationally close to the half-filled non-magnetic Mott insulator. Superconductivity exists at half-filling just at the border of the Mott transition and extends away from half-filling into a whole region till a critical doping, beyond which it gives way to a normal metal phase. This res…
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…
Using the real-space Hartree Fock approximation, the magnetic phase diagram of a five-orbital Hubbard model for the iron-based superconductors is studied varying the electronic density $n$ in the range from 5 to 7 electrons per transition metal atom. The Hubbard interaction $U$ is also varied, at a fixed Hund coupling $J/U=0.25$. Several qualitative trends and a variety of competing magnetic states are observed. At $n$=5, a robust G-type antiferromagnetic insulator is found, in agreement with experimental results for BaMn$_2$As$_2$. As $n$ increases away from 5, magnetic states with an increas…
Motivated by superconductivity (SC) in layered nitrides, we study an ionic-Hubbard model on a honeycomb lattice, which consists of two sublattices with an energy-level offset, by using an optimization variational Monte Carlo method. Parameter values for the Coulomb interaction and the energy-level offset, to realize a band insulator in non-doped state, are evaluated, and the SC state is investigated in a carrier-doped band insulator. It is found that, in a weakly doped band insulator, spin fluctuation remains and the spin-singlet d-wave SC state is realized. Present results support an unconven…
We introduce a {\em local} formalism, in terms of eigenstates of number operators, having well defined point symmetry, to solve the Hubbard model at weak coupling on a $N\times N$ square lattice (for even $N$). The key concept is that of W=0 states, that are the many-body eigenstates of the kinetic energy with vanishing Hubbard repulsion. At half filling, the wave function demonstrates an antiferromagnetic order, a lattice step translation being equivalent to a spin flip. Further, we state a general theorem which allows to find all the W=0 pairs (two-body W=0 singlet states). We show that, in …
We study, using a perturbative renormalization group technique, the phase diagrams of bond-aligned and diagonal Hubbard ladders defined as sections of a square lattice with nearest-neighbor and next-nearest-neighbor hopping. We find that for not too large hole doping and small next-nearest-neighbor hopping the bond-aligned systems exhibit a fully spin-gapped phase while the diagonal systems remain gapless. Increasing the next-nearest-neighbor hopping typically leads to a decrease of the gap in the bond-aligned ladders, and to a transition into a gapped phase in the diagonal ladders. Embedding …
Cluster perturbation theory is used to calculate band structure, spectral functions, Fermi surface, and spin and charge susceptibilities for the two-orbital model of iron pnictides with the on-site multiorbital Hubbard interactions. Susceptibilities are calculated within the approximation combining the cluster perturbation theory for the self-energy corrections and the random-phase approximation (RPA) for the vertex renormalizations. Calculations for the small values of Hubbard repulsion $U \leq 2$ confirm that the rigid band approximation and RPA for the spin and charge susceptibilities are s…
