Single-band Hubbard Model Research Articles

Metal-Insulator Transitions in the Periodic Anderson Model

We solve the periodic Anderson model in the Mott-Hubbard regime, using dynamical mean field theory. Upon electron doping of the Mott insulator, a metal-insulator transition occurs which is qualitatively similar to that of the single band Hubbard model, namely, with a divergent effective mass and a first order character at finite temperatures. Surprisingly, upon hole doping, the metal-insulator transition is not first order and does not show a divergent mass. Thus, the transition scenario of the single band Hubbard model is not generic for the periodic Anderson model, even in the Mott-Hubbard regime.

Rotationally invariant slave-boson formalism and momentum dependence of the quasiparticle weight

We generalize the rotationally invariant formulation of the slave-boson formalism to multiorbital models, with arbitrary interactions, crystal fields, and multiplet structure. This allows for the study of multiplet effects on the nature of low-energy quasiparticles. Nondiagonal components of the matrix of quasiparticle weights can be calculated within this framework. When combined with cluster extensions of dynamical mean-field theory, this method allows us to address the effects of spatial correlations, such as the generation of the superexchange and the momentum dependence of the quasiparticle weight. We illustrate the method on a two-band Hubbard model, a Hubbard model made of two coupled layers, and a two-dimensional single-band Hubbard model (within a two-site cellular dynamical mean-field approximation).

Effect of Uniaxial Pressure on the Isotope Effect on the Spectrum of Hamiltonians with Electron–Phonon Coupling

We have studied the effect of a change in the equilibrium nearest neighbour distances on the dynamics of charge and ions on a three-site cluster, identified with an O–Cu–O cluster present in high temperature superconductors. We consider a model Hamiltonian that contains an electronic part represented by a single band Hubbard model with onsite electronic correlations and a phononic part consisting of non-interacting Raman and infrared active phonons. The electron–phonon coupling is introduced through the change in interatomic distances generated by Coulomb repulsion between charges at neighbouring sites. For intermediate and strong values of the electron–phonon coupling, this model generates correlated electron–ion motion, i.e., polaron formation. In order to simulate the effect of change in the equilibrium nearest neighbour distances, we assume that the main effect such a change is a variation of the intersite electron hopping probability, t. We, therefore, studied the excitation spectrum of this model and the local lattice distortion in the Cu–O bond length as a function of t. We also studied the effect of a change in t in the polaron tunnelling energy when we use different oxygen isotopic masses, i.e., O16 and O18. We find that as function of t, the isotopic shift does not show a monotonic behaviour, as it does as a function of the electron–phonon coupling constant. It exhibits a minimum for values of t for which the electron–phonon coupling generates local lattice distortions with magnitudes similar to those observed experimentally in high-temperature superconductors. This observation could be related with the observed maximum on Tc as a function of the microstrain of the Cu–O bonds (Sanna et al. in Int. J. Mod. Phys. B 14(29–31), 2000; Bianconi et al. in J. Phys.: Condens. Matter 12:10655, 2000; Agrestini et al. in J. Phys. A: Math. Gen. 36:9133, 2003).

Variational Monte Carlo study of pairing symmetry in Sr2RuO4

With a mind to superconductivity (SC) arising in Sr2RuO4, we study a Hubbard model on square lattice including second-neighbor hopping t′, using an optimization variational Monte Carlo method. As a pairing state, we have chosen dx2-y2(d) wave for singlet and px (p)-wave for triplet pairing state. In the trial wave functions, a doublon–holon binding effect is introduced in addition to the onsite Gutzwiller projection. By calculating condensation energies of the SC states, we found that when t′=−0.4t, the d-wave state is stabilized against the normal state for 0.6<n<1. On the other hand, p-wave state is never stabilized in this regime. Based on this result, it is difficult to understand a spin-triplet state simply from the single-band Hubbard model with onsite Coulomb interaction.

Wannier functions and exchange integrals: The example ofLiCu2O2

Starting from a single band Hubbard model in the Wannier function basis, we revisit the problem of the ligand contribution to exchange and derive explicit formulas for the exchange integrals in metal oxide compounds in terms of atomic parameters that can be calculated with constrained LDA and $\mathrm{LDA}+\mathrm{U}$. The analysis is applied to the investigation of the isotropic exchange interactions of $\mathrm{Li}{\mathrm{Cu}}_{2}{\mathrm{O}}_{2}$, a compound where the Cu-O-Cu angle of the dominant exchange path is close to 90\ifmmode^\circ\else\textdegree\fi{}. Our results show that the magnetic moments are localized in Wannier orbitals which have strong contribution from oxygen atomic orbitals, leading to exchange integrals that considerably differ from the estimates based on kinetic exchange only. Using $\mathrm{LSDA}+\mathrm{U}$ approach, we also perform a direct ab initio determination of the exchange integrals $\mathrm{Li}{\mathrm{Cu}}_{2}{\mathrm{O}}_{2}$. The results agree well with those obtained from the Wannier function approach, a clear indication that this modelization captures the essential physics of exchange. A comparison with experimental results is also included, with the conclusion that a very precise determination of the Wannier function is crucial to reach quantitative estimates.

Phase diagram of half-filled square lattice for frustrated Hubbard model

Although the single-band Hubbard model for a half-filled square lattice is considered to be an antiferromagnetic (AF) insulator, it is a current vital question to ask what happens if the second nearest-neighbor hopping (t′) is introduced to it. To study this problem, we use the fluctuation exchange (FLEX) approximation together with the variational Monte Carlo (VMC) method. We have obtained basically consistent results: A first-order Mott transition takes place at the Coulomb repulsion U=Uc for a wide range of t′, and robust d-wave SC whose transition temperature is more than 0.01t (t is the nearest-neighbor hopping) appears near the AF and the Mott insulator region. We have also found that the superconductivity as well as an AF long-range order is suppressed as t′ increases, because the AF spin fluctuation becomes weaker.

Checkerboard and stripe inhomogeneities in cuprates

We systematically investigate charge-ordering phases by means of a restricted and unrestricted Gutzwiller approximation to the single-band Hubbard model with nearest- $(t)$ and next-nearest- $({t}^{\ensuremath{'}})$ neighbor hopping. When $\ensuremath{\mid}{t}^{\ensuremath{'}}∕t\ensuremath{\mid}$ is small, as appropriate for ${\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}\mathrm{Cu}{\mathrm{O}}_{4}$, stripes are found, whereas in compounds with larger $\ensuremath{\mid}{t}^{\ensuremath{'}}∕t\ensuremath{\mid}$ (such as ${\mathrm{Ca}}_{2\ensuremath{-}x}{\mathrm{Na}}_{x}\mathrm{Cu}{\mathrm{O}}_{2}{\mathrm{Cl}}_{2}$ and ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}\mathrm{Ca}{\mathrm{Cu}}_{2}{\mathrm{O}}_{8+\ensuremath{\delta}}$) checkerboard structures are favored. In contrast to the linear doping dependence found for stripes the charge periodicity of checkerboard textures is locked to $4\phantom{\rule{0.3em}{0ex}}\text{unit}$ cells over a wide doping range. In addition we find that checkerboard structures are favored at surfaces.

Superconducting phase diagram in a model for tetragonal and cubic systems with strong antiferromagnetic correlations

We calculate the superconducting phase diagram as a function of temperature and $z$-axis anisotropy in a model for tetragonal and cubic systems having strong antiferromagnetic fluctuations. The formal basis for our calculations is the fluctuation exchange approximation applied to the single-band Hubbard model near half-filling. For nearly cubic lattices, two superconducting phase transitions are observed as a function of temperature with the low-temperature state having the time-reversal symmetry-breaking form ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}\ifmmode\pm\else\textpm\fi{}i{d}_{3{z}^{2}\ensuremath{-}{r}^{2}}$. With increasing tetragonal distortion, the time-reversal symmetry-breaking phase is suppressed, giving way to only ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ or ${d}_{3{z}^{2}\ensuremath{-}{r}^{2}}$ single-component phases. Based on these results, we propose that a time-reversal symmetry-breaking superconducting state may be found in cubic systems with pairing driven by antiferromagnetic fluctuations.

Theoretical Study of the Phase Diagram of β'-(BEDT-TTF)2AuCl2at Hydrostatic Pressure

We study the electronic structure of β'-(BEDT-TTF) 2 AuCl 2 under hydrostatic pressures of up to 20 GPa. We employ the effective single-band Hubbard model, the band structure of which is based on the first-principles result, and apply the FLEX approximation to take into account of the effective on-site Coulomb interaction. We examine magnetic and superconducting instabilities to find that the resulting theoretical phase diagram shows that the Neel temperature is high under hydrostatic pressure. In contrast to β'-(BEDT-TTF) 2 ICl 2 , β'-(BEDT-TTF) 2 AuCl 2 is expected to show no superconducting state.

Transfer of Spectral Weight and Symmetry across the Metal-Insulator Transition inVO2

We present a detailed study of the valence and conduction bands of VO2 across the metal-insulator transition using bulk-sensitive photoelectron and O K x-ray absorption spectroscopies. We observe a giant transfer of spectral weight with distinct features that require an explanation which goes beyond the Peierls transition model as well as the standard single-band Hubbard model. Analysis of the symmetry and energies of the bands reveals the decisive role of the V 3d orbital degrees of freedom. Comparison to recent realistic many body calculations shows that much of the k dependence of the self-energy correction can be cast within a dimer model.

Stripe phases—possible ground state of the high-Tc superconductors

Based on the mean-field method applied either to the extended single-band Hubbard model or to the single-band Peierls–Hubbard Hamiltonian we study the stability of both site-centered and bond-centered charge domain walls. The difference in energy between these phases is found to be small. Therefore, moderate perturbations to the pure Hubbard model, such as next-nearest-neighbor hopping, lattice anisotropy, or coupling to the lattice, induce phase transitions, shown in the corresponding phase diagrams. In addition, we determine the charge for stable phases and magnetization densities, double occupancy, and kinetic and magnetic energies and investigate the role of a finite electron-lattice coupling. We also review experimental signatures of stripes in the superconducting copper oxides.

Phase separation and pseudogap in electron-doped cuprates: A variational cluster perturbation analysis

We study the quantum transition from an antiferromagnet to a superconductor in the single-band Hubbard model with parameters appropriate to describe electron- and hole-doped cuprates by means of variational cluster perturbation theory, a method appropriate to deal with strongly-correlated systems. In both cases, our results produce phase separation into a mixed antiferromagnetic-superconducting phase at low doping and a pure superconducting (SC) phase at higher doping. However, in the electron-doped case the energy scale for phase separation is an order of magnitude smaller than for hole doping. This behavior can be understood in terms of the different Fermi-surface evolution in p- and n-doped materials upon doping. We argue that this behavior can be related to the different pseudogap and SC transition scales in hole- and electron-doped materials.

Theory on photoemission and inverse photoemission spectra in [formula omitted

The photoemission (PES) and inverse photoemission (IPES) spectra in VO 2 at temperatures above and below the metal–insulator transition (MIT) are discussed with a two-band Hubbard model. An abrupt change in the valence top character of the theoretical PES spectra at the MIT caused by a switching in the t 2 g orbital occupation in the ground state is found. In the insulating phase, the structure of the valence top is well described within a single-band Hubbard model, where only the d | | band participates. Since the ratio t / U ∼ 0.2 is small, the structure of the spectrum extends to ∼ 1.5 eV below the Fermi level. On the other hand, in the metallic phase, both the d | | and π * bands are involved and the spectral weight is concentrated in the vicinity of the Fermi level within a range ∼ 0.5 eV . Such a large spectral weight transfer is consistent with experiments. For the IPES spectra, a structure corresponding to the upper Hubbard band of the single-band Hubbard model is appeared at ∼ 1.5 eV above the Fermi level in the insulating phase. However the structure is absent in the metallic phase.

Sum rules for inelastic light scattering in the Hubbard model

The f-sum rule for the optical conductivity has been known for many years, and has found widespread use in a number of different fields of science. In this contribution, we show how the f-sum rule can be generalized to inelastic light scattering and we explicitly derive the form of the sum rule for the single-band Hubbard model. We discuss evidence that indicates such a sum rule likely holds in already calculated dynamical mean-field theory results and we describe evidence in support of these new sum rules in electronic Raman scattering data for SmB 6 .

Role of electron-phonon interaction on quasiparticle dispersion in the strongly correlated cuprate superconductors

The role of the electron-phonon (el-ph) interaction in high-${T}_{c}$ cuprates is investigated theoretically by considering correlated electrons interacting with Holstein phonons within the two-dimensional single-band Hubbard model in the limit of large Coulomb interaction. It is shown that the electron-phonon interaction gives rise to a kink in the dispersion along the nodal direction and to a peak/dip/hump structure in the one-electron spectral weight whose dependence on temperature, isotope substitution, and doping is discussed in relation to recent photoemission experiments on the nodal quasiparticles in Bi2201 and LSCO. A comparison with these experiments shows that electron correlations play a crucial role in the determination of the kink position, size, and doping dependence. We also show that the ``unusual'' oxygen isotope shift in the real part of the self-energy, experimentally observed in the optimally doped Bi2212 samples, can be qualitatively explained within the framework that incorporates both strong electron correlations and the adiabatic electron-phonon interaction.

Theory of RIXS in strongly correlated electron systems: Mott gap excitations in cuprates

We theoretically examine the momentum dependence of resonant inelastic x-ray scattering (RIXS) spectrum for one-dimensional and two-dimensional cuprates based on the single-band Hubbard model with realistic parameter values. The spectrum is calculated by using the numerical diagonalization technique for finite-size clusters. We focus on excitations across the Mott gap and clarify spectral features coming from the excitations as well as the physics behind them. Good agreement between the theoretical and existing experimental results clearly demonstrates that the RIXS is a potential tool to study the momentum-dependent charge excitations in strongly correlated electron systems.

Hidden ferrimagnetism in pniktides (Fe–Mn)1.95As

The results of experimental investigations of the magnetic properties of the antiferromagnetic alloy Fe0.765Mn1.185As are presented. They show that at atmospheric pressure and temperatures below 65 K the antiferromagnetic state is not the only stable state, since the imposition of a magnetic field in this temperature range makes it possible to observe irreversible induced transitions into a state with a canted ferrimagnetic structure. This is a second stable state for the experimental sample. As the temperature increases, this state vanishes via a first-order phase transformation at 65 K. Above 65 K reversible induced first-order transitions from the antiferromagnetic into a canted ferrimagnetic structure are observed. The results are discussed on the basis of a phenomenological expression for the free energy of a system with two interacting magnetic-order parameters. It is shown that a simple phenomenological model qualitatively describes the behavior of the system investigated. A single-band Hubbard model is used to give a microscopic substantiation of the phenomenological approach.

Experimental study on thickness-related electrical characteristics in organic/metal-nanocluster/organic systems

Organic bistable devices with the trilayer structure, organic/metal-nanocluster/organic, interposed between two electrodes have been systematically studied by varying the thickness of the organic layers and the metal-nanocluster layer. Devices fabricated in this fashion exhibit either electrical bistability or current step, depending on the thickness of the metal-nanocluster layer. Electrical bistable devices have been studied by fixing the metal-nanocluster layer thickness at 20 nm and changing the organic-layer thickness from 20 to 60 nm. Device injection current at the on state shows an exponential decrease with an increasing organic-layer thickness, suggesting that the electron transmission probability of the devices decreases with an increasing thickness of the organic layer. This is in agreement with theoretical calculations based on the single-band Hubbard model. The evolution of the electrical current step is observed for devices fabricated by fixing the organic-layer thickness at 50 nm and changing the metal-nanocluster layer thicknesses (2, 4, and 8 nm). The discontinuous metal-nanocluster layer is believed to lead to the observed current step. When the metal-nanocluster layer is thick enough resonant tunneling occurs between nanoclusters causing positive and negative charges to be stored on the opposite sides of the metal-nanocluster layer inducing electrical bistability. Discussions of the observed phenomena are presented.

Benchmarkings for a semiclassical impurity solver for dynamical-mean-field theory: Self-energies and magnetic transitions of the single-orbital Hubbard model

An investigation is presented of the utility of semiclassical approximations for solving the quantum-impurity problems arising in the dynamical-mean-field approach to the correlated-electron models. The method is based on performing a exact numerical integral over the zero-Matsubara-frequency component of the spin part of a continuous Hubbard-Stratonovich field, along with a spin-field-dependent steepest descents treatment of the charge part. We test this method by applying it to one or two site approximations to the single band Hubbard model with different band structures, and comparing the results to quantum Monte-Carlo and simplified exact diagonalization calculations. The resulting electron self-energies, densities of states and magnetic transition temperatures show reasonable agreement with the quantum Monte-Carlo simulation over wide parameter ranges, suggesting that the semiclassical method is useful for obtaining a reasonable picture of the physics in situations where other techniques are too expensive.

Physics of cuprates with the two-band Hubbard model: The validity of the one-band Hubbard model

We calculate the properties of the two-band Hubbard model using the dynamical cluster approximation. The phase diagram resembles the generic phase diagram of the cuprates, showing a strong asymmetry with respect to electron- and hole-doped regimes, in agreement with experiment. Asymmetric features are also seen in one-particle spectral functions and in the charge, spin, and $d$-wave pairing-susceptibility functions. We address the possible reduction of the two-band model to a low-energy single-band one, as it was suggested by Zhang and Rice. Comparing the two-band Hubbard model properties with the single-band Hubbard model ones, we have found similar low-energy physics provided that the next-nearest-neighbor hopping term ${t}^{\ensuremath{'}}$ has a significant value $({t}^{\ensuremath{'}}∕t\ensuremath{\approx}0.3)$. The parameter ${t}^{\ensuremath{'}}$ is the main culprit for the electron-hole asymmetry. However, a significant value of ${t}^{\ensuremath{'}}$ cannot be provided in a strict Zhang and Rice [Phys. Rev. B 37, R3759 (1988); 41, 7243 (1990)] picture where the extra holes added into the system bind to the existing Cu holes forming local singlets. We note that by considering approximate singlet states, such as plaquette states, reasonable values of ${t}^{\ensuremath{'}}$, which capture qualitatively the physics of the two-band model, can be obtained. We conclude that a single-band $t\text{\ensuremath{-}}{t}^{\ensuremath{'}}\text{\ensuremath{-}}U$ Hubbard model captures the basic physics of the cuprates concerning superconductivity, antiferromagnetism, pseudogap, and electron-hole asymmetry, but is not suitable for a quantitative analysis or to describe physical properties involving energy scales larger than about 0.5 eV.