Two-orbital Hubbard Model Research Articles

Spin fluctuations and orbital-selective superconductivity in Ba2CuO4-y: A FLEX study

Abstract Recently discovered Ba2CuO4-y provides new perspectives to the study of high-temperature superconductivity. Whereas, little is known about the spin dynamics of this material. In this work, we employ the fluctuation exchange (FLEX) approximation within the framework of spin-fluctuation mediated superconductivity to examine the behavior of the spin fluctuations of a two-orbital Hubbard model for Ba2CuO4-y. Our calculations reveal an extraordinary spin resonance mode coupled to the superconducting state in the hole-underdoped regime. Furthermore, we confirm that the coupling between the electrons and this resonance mode can lead to a “dip”-like feature in the electronic spectrum as a feedback effect. In the hole-overdoped regime, by incorporating self energy into our calculations, we obtain orbital-dependent renormalizations and show how these self-energy effects can lead to the detailed gap structures and the orbital-selective superconductivity, which could not be obtained in a previous study using random phase approximation (RPA). This research may shed a new light on searching for unconventional superconductors with higher transition temperatures.

Effects of Magnetic Fields and Orbital Angular Momentum on Excitonic Condensation in Two-Orbital Hubbard Model

Effects of Magnetic Fields and Orbital Angular Momentum on Excitonic Condensation in Two-Orbital Hubbard Model

The interplay of field-tunable strongly correlated states in a multi-orbital moiré system

The interplay of charge, spin, lattice and orbital degrees of freedom leads to a variety of emergent phenomena in strongly correlated systems. In transition-metal-dichalcogenide-based moiré heterostructures, recent observations of correlated phases can be described by triangular-lattice single-orbital Hubbard models based on moiré bands derived from the Brillouin-zone corners—the so-called K valleys. Richer phase diagrams described by multi-orbital Hubbard models are possible with hexagonal lattices that host moiré bands at the zone centre—called Γ valleys—or an additional layer degree of freedom. Here we report the tunable interaction between strongly correlated hole states hosted by Γ- and K-derived bands in a heterostructure of monolayer MoSe2 and bilayer 2H WSe2. We characterize the behaviour of exciton–polarons to distinguish the layer and valley degrees of freedom. The Γ band gives rise to a charge-transfer insulator described by a two-orbital Hubbard model. An out-of-plane electric field re-orders the Γ- and K-derived bands and drives the redistribution of carriers to the layer-polarized K orbital, generating Wigner crystals and Mott insulating states. Finally, we obtain degeneracy of the Γ and K orbitals at the Fermi level and observe interacting correlated states with phase transitions dependent on the doping density. Our results establish a platform to investigate multi-orbital Hubbard model Hamiltonians.

Transition to the Haldane phase driven by electron-electron correlations

One of the most famous quantum systems with topological properties, the spin S=1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{{{{{{\\mathcal{S}}}}}}}}=1$$\\end{document} antiferromagnetic Heisenberg chain, is well-known to display exotic S=1/2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{{{{{{\\mathcal{S}}}}}}}}=1/2$$\\end{document} edge states. However, this spin model has not been analyzed from the more general perspective of strongly correlated systems varying the electron-electron interaction strength. Here, we report the investigation of the emergence of the Haldane edge in a system of interacting electrons – the two-orbital Hubbard model—with increasing repulsion strength U and Hund interaction JH. We show that interactions not only form the magnetic moments but also form a topologically nontrivial fermionic many-body ground-state with zero-energy edge states. Specifically, upon increasing the strength of the Hubbard repulsion and Hund exchange, we identify a sharp transition point separating topologically trivial and nontrivial ground-states. Surprisingly, such a behaviour appears already at rather small values of the interaction, in a regime where the magnetic moments are barely developed.

Many-body correlations in one-dimensional optical lattices with alkaline-earth(-like) atoms

We explore the rich nature of correlations in the ground state of ultracold atoms trapped in state-dependent optical lattices. In particular, we consider interacting fermionic ytterbium or strontium atoms, realizing a two-orbital Hubbard model with two spin components. We analyze the model in one-dimensional setting with the experimentally relevant hierarchy of tunneling and interaction amplitudes by means of exact diagonalization and matrix product states approaches, and study the correlation functions in density, spin, and orbital sectors as functions of variable densities of atoms in the ground and metastable excited states. We show that in certain ranges of densities these atomic systems demonstrate strong density-wave, ferro- and antiferromagnetic, as well as antiferroorbital correlations.

Spin-orbital correlations in the two-orbital Hubbard model

We use exact diagonalization results to investigate how the ground state of a two-site, two-orbital Hubbard model evolves in terms of the crystal field energy and a magnetic spin symmetry breaking field. We show that, based on the behavior of a properly defined composite spin-orbital correlation function, the different regions of the related phase diagrams can be classified according to the extent to which spin and orbital degrees of freedom turn out to be correlated.

Extended regime of metastable metallic and insulating phases in a two-orbital electronic system

Taking the nonlocal collective electronic fluctuations into account completely changes the state-of-the-art scenario for the metal-insulator transition in a quarter-filled two-orbital Hubbard model. These fluctuations redistribute the spectral weight between the orbitals, which results in an extremely broad coexistence region between the metallic and Mott insulating states.

Competing correlated insulators in multiorbital systems coupled to phonons

We study the interplay between electron-electron interaction and a Jahn-Teller phonon coupling in a two-orbital Hubbard model. We demonstrate that the e-ph interaction coexists with the Mott localization driven by the Hubbard repulsion $U$, but it competes with the Hund's coupling $J$. This interplay leads to two spectacularly different Mott insulators, a standard high-spin Mott insulator with frozen phonons which is stable when the Hund's coupling prevails, and a low-spin Mott-bipolaronic insulator favored by phonons, where the characteristic features of Mott insulators and bipolarons coexist. The two phases are separated by a sharp boundary along which an intriguing intermediate solution emerges as a kind of compromise between the two solutions.

Orbital correlations in ultrathin films of late transition metals

We develop a two-orbital Hubbard model of electron correlations in ultrathin (111)-oriented fcc films of late transition metals such as Co and Ni. Our model indicates that the Mott-Hund's interaction results in ferromagnetic nearest-neighbor orbital correlations. Frustration associated with the mismatch between orbital and crystal symmetries prevents orbital ordering, resulting in the orbital liquid state. This state can be manifested in phenomena involving spin-orbit coupling, such as magnetic anisotropy.

Parameter-free analytic continuation for quantum many-body calculations

We develop a reliable parameter-free analytic continuation method for quantum many-body calculations. Our method is based on a kernel grid, a causal spline, a regularization using the second-derivative roughness penalty, and the L-curve criterion. We also develop the L-curve averaged deviation to estimate the precision of our analytic continuation. To deal with statistically obtained data more efficiently, we further develop a bootstrap-averaged analytic continuation method. In the test using the exact imaginary-frequency Green's function with added statistical error, our method produces the spectral function that converges systematically to the exact one as the statistical error decreases. As an application, we simulate the two-orbital Hubbard model for various electron numbers with the dynamical-mean field theory in the imaginary time and obtain the real-frequency self-energy with our analytic continuation method, clearly identifying a non-Fermi liquid behavior as the electron number approaches the half filling from the quarter filling. Our analytic continuation can be used widely and it will facilitate drawing clear conclusions from imaginary-time quantum many-body calculations.

Enhanced Spin–Orbit Coupling in a Correlated Metal

We investigate the correlation effects on spin-orbit coupling (SOC) in a two-orbital Hubbard model on a square lattice by applying the variational Monte Carlo method. We consider an effective SOC constant $\lambda_{\text{eff}}$ in the one-body part of the variational wave function and mainly discuss the cases of the electron number per site $n=1$, that is, quarter filling. We find that $\lambda_{\text{eff}}$ is proportional to the bare value $\lambda$ and depends on the electron-electron interactions through $(U'-J')$ in a relatively wide parameter range in the paramagnetic (PM) phase, where $U'$ is the interorbital Coulomb interaction and $J'$ is the pair hopping interaction. Increasing the electron-electron interactions in the PM phase leads to a transition to an effective one-band state, in which the upper band becomes empty due to the enhanced $\lambda_{\text{eff}}$. We also construct phase diagrams considering magnetic order. The carrier doping effect on $\lambda_{\text{eff}}$ is also investigated. We find that $\lambda_{\text{eff}}$ enhances in a strongly correlated region around the Mott transition point and it is necessary to include the correlation effects beyond the Hartree-Fock approximation to describe the enhanced SOC properly.

Excitonic Correlations, Spin-State Ordering, and Magnetic-Field Effects in One-Dimensional Two-Orbital Hubbard Model for Spin-Crossover Region

The electronic properties of excitonic insulators have been examined precisely in recent years. Pictures of exciton condensation may be applied to the spin-state transition observed in perovskite cobalt oxides. We examine the crystal-field and magnetic-field dependences of spatial spin structures on the basis of the density matrix renormalization group method using an effective model for the one-dimensional two-orbital Hubbard model in strong-coupling limit. We find an excitonic insulating (EI) phase and a spin-state ordering (SSO) phase in the intermediate region between low-spin and high-spin phases. In the EI phase, spin-triplet excitons are spatially fluctuating due to quantum effects, and an incommensurate spin correlation realizes. The analyses of a spin gap and degeneracy of entanglement spectra suggest the realization of the Haldane-like edge state in the EI phase. In the SSO phase, 3-fold or incommensurate SSO structures realize depending on the crystal-field splitting. These structures are stabilized as a result of the competition of exchange interactions between spin states.

Local interpretation of time-resolved x-ray absorption in Mott insulators: Insights from nonequilibrium dynamical mean-field theory

We present a formalism based on nonequilibrium dynamical mean field theory (DMFT) which allows to compute the time-resolved X-ray absorption spectrum (XAS) of photo-excited solids. By applying this formalism to the photo-doped half-filled and quarter-filled two-orbital Hubbard models in the Mott insulating regime we clarify how the time-resolved XAS signal reflects the nonequilibrium population of different local states. Apart from the missing broadening associated with continuum excitations, the atomic XAS spectrum computed with the nonthermal state populations provides a good approximation to the full nonequilibrium DMFT result. This suggest a route to combine the accurate DMFT description of nonequilibrum states of solids with cluster calculations of the XAS signal.

Band crossover and magnetic phase diagram of the high- Tc superconducting compound Ba2CuO4−δ

We present the influences of electronic and magnetic correlations and doping evolution on the groundstate properties of recently discovered superconductor Ba$_{2}$CuO$_{4-\delta}$ by utilizing the Kotliar-Ruckenstein slave boson method. Starting with an effective two-orbital Hubbard model (Scalapino {\it et al.} Phys. Rev. {\bf B 99}, 224515 (2019)), we demonstrate that with increasing doping concentration, the paramagnetic (PM) system evolves from two-band character to single-band ones around the electron filling n=2.5, with the band nature of the $d_{3z^{2}-r^{2}}$ and $d_{x^{2}-y^{2}}$ orbitals to the $d_{x^{2}-y^{2}}$ orbital, slightly affected when the electronic correlation U varies from 2 to 4 eV. Considering the magnetic correlations, the system displays one antiferromagnetically metallic (AFM) phase in $2<n<2.16$ and a PM phase in $n>2.16$ at U=2 eV, or two AFM phases in $2<n<2.57$ and $2.76<n<3$, and a PM phase in $2.57<n<2.76$ respectively, at U=4 eV. Our results show that near realistic superconducting state around n=2.6 the intermediate correlated Ba$_{2}$CuO$_{3,2}$ should be single band character, and the s-wave superconducting pairing strength becomes significant when U$>$2 eV, and crosses over to d-wave when U$>$2.2 eV.

Photoinduced dynamics of a quasicrystalline excitonic insulator

We study the photoinduced dynamics of the excitonic insulator in the two-orbital Hubbard model on the Penrose tiling by means of the time-dependent real-space mean-field approximation. We show that, with a single-cycle electric-field pulse, the bulk (spatially averaged) excitonic order parameter decreases in the Bardeen-Cooper-Schrieffer (BCS) regime, while it increases in the Bose-Einstein condensate (BEC) regime. This behavior is in common with the excitonic insulator in the square lattice reported previously. To explore the dynamics peculiar to the Penrose tiling, we examine the coordination number dependence of observables and analyze the perpendicular space. In the BEC regime, characteristic oscillations of the electron number at each site are induced by the pulse, which are not observed in normal crystals with single coordination number. On the other hand, the dynamics in the BCS regime is characterized by drastic change in the spatial pattern of the excitonic order parameter. Our results imply that potentially interesting nonequilibrium physics is caused by rich local structural patterns involved in quasicrystals.

Dynamical mean-field theory of two-orbital Hubbard model

The effect of interorbital hopping on orbital selective Mottness in a two-band correlation system is investigated by using the dynamical mean-field theory with the Lanczos method as impurity solver. The phase diagrams of the two-orbital Hubbard model with non-local interorbital hopping (&lt;i&gt;t&lt;/i&gt;&lt;sub&gt;12&lt;/sub&gt;) , where the orbital selective Mott phases (OSMP) region is expanded by the increasing of the interorbital hopping. We compare the results obtained by self-consistent relations of Bethe lattice and squate lattice based on DMFT procedure, and the general OSMP physics of Bethe lattice is consistent with that of the square lattice while the critical points of two kinds of lattices are different. We extend the method to the study of half-filled Ba&lt;sub&gt;2&lt;/sub&gt;CuO&lt;sub&gt;4–&lt;i&gt;δ&lt;/i&gt;&lt;/sub&gt; materials. By comparing with the band structure obtained from the density functional theory (DFT), it is found that the isotropic inter-orbital hopping has a great influence on the bandstructure. The DFT bandstructure in DMFT is considered, and the phase diagram of the material is obtained. The half-filled Ba&lt;sub&gt;2&lt;/sub&gt;CuO&lt;sub&gt;4–&lt;i&gt;δ&lt;/i&gt;&lt;/sub&gt; should be orbital-selective Mott compound according to our results.

Excitonic wave-packet evolution in a two-orbital Hubbard model chain: A real-time real-space study

Motivated by experimental developments introducing the concept of spin-orbit separation, we study the real-space time evolution of an excitonic wave-packet using a two-orbital Hubbard model. The exciton is created by exciting an electron from a lower energy half-filled orbital to a higher energy empty orbital. We carry out the real-time dynamics of the resulting excitonic wave-packet, using the time-dependent density matrix renormalization group method. We find clear evidence of charge-spin and spin-orbit separation in real-space, by tracking the time evolution of local observables. We show that the velocity of the orbiton can be tuned by varying the inter-orbital interactions. We also present a comparative study of a hole (in one orbital) and exciton (in two orbitals) dynamics in one-dimensional systems. Moreover, we analyze the dynamics of an exciton with spin-flip excitation, where we observe fractionalized spinons induced by Hund's interaction.

Intertwined charge, spin, and pairing orders in doped iron ladders

Motivated by recent experimental progress on iron-based ladder compounds, we study the doped two-orbital Hubbard model for the two-leg ladder BaFe$_2$S$_3$. The model is constructed by using {\it ab initio} hopping parameters and the ground state properties are investigated using the density matrix renormalization group method. We show that the $(\pi,0)$ magnetic ordering at half-filling, with ferromagnetic rungs and antiferromagnetic legs, becomes incommensurate upon hole doping. Moreover, depending on the strength of the Hubbard $U$ coupling, other magnetic patterns, such as $(0,\pi)$, are also stabilized. We found that the binding energy for two holes becomes negative for intermediate Hubbard interaction strength, indicating hole pairing. Due to the crystal-field split among orbitals, the holes primarily reside in one orbital, with the other one remaining half-filled. This resembles orbital selective Mott states. The formation of tight hole pairs continues with increasing hole density, as long as the magnetic order remains antiferromagnetic in one direction. The study of pair-pair correlations indicates the dominance of the intra-orbital spin-singlet channel, as opposed to other pairing channels. Although in a range of hole doping pairing correlations decay slowly, our results can also be interpreted as corresponding to a charge-density-wave made of pairs, a precursor of eventual superconductivity after interladder couplings are included. Such scenario of intertwined orders has been extensively discussed before in the cuprates, and our results suggest a similar physics could exist in ladder iron-based superconductors. Finally, we also show that a robust Hund's coupling is needed for pairing to occur.

Electronic correlation-driven orbital polarization transitions in the orbital-selective Mott compound Ba2CuO4−δ

The electronic states near the Fermi level of recently discovered superconductor ${\mathrm{Ba}}_{2}{\mathrm{CuO}}_{4\ensuremath{-}\ensuremath{\delta}}$ consist primarily of the Cu ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ and ${d}_{3{z}^{2}\ensuremath{-}{r}^{2}}$ orbitals. We investigate the electronic correlation effect and the orbital polarization of an effective two-orbital Hubbard model mimicking the low-energy physics of ${\mathrm{Ba}}_{2}{\mathrm{CuO}}_{4\ensuremath{-}\ensuremath{\delta}}$ in the hole-rich regime by utilizing the dynamical mean-field theory with the Lanczos method as the impurity solver. We find that the hole-overdoped ${\mathrm{Ba}}_{2}{\mathrm{CuO}}_{4\ensuremath{-}\ensuremath{\delta}}$ with $3{d}^{8}$ (${\mathrm{Cu}}^{3+}$) is in the orbital-selective Mott phase (OSMP) at half-filling, and the typical two-orbital feature remains in ${\mathrm{Ba}}_{2}{\mathrm{CuO}}_{4\ensuremath{-}\ensuremath{\delta}}$ when the electron filling approaches ${n}_{e}\ensuremath{\sim}2.5$, which closely approximates to the experimental hole doping for the emergence of the high-${T}_{c}$ superconductivity. We also obtain that the orbital polarization is very stable in the OSMP, and the multiorbital correlation can drive orbital polarization transitions. These results indicate that in hole-overdoped ${\mathrm{Ba}}_{2}{\mathrm{CuO}}_{4\ensuremath{-}\ensuremath{\delta}}$ the OSMP physics and orbital polarization, local magnetic moment, and spin or orbital fluctuations still exist. We propose that our present results are also applicable to ${\mathrm{Sr}}_{2}{\mathrm{CuO}}_{4\ensuremath{-}\ensuremath{\delta}}$ and other two-orbital cuprates, demanding an unconventional multiorbital superconducting scenario in hole-overdoped high-${T}_{c}$ cuprates.

Hund Physics Landscape of Two-Orbital Systems.

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 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 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, which we call "intermediate" metal, weak Hund metal, and valence-skipping metal, from the effect of J being away from Mottness. Defining criteria characterizing these metals is suggested, establishing the existence of Hund metallicity in two-orbital systems.