Variational local moment approach: From Kondo effect to Mott transition in correlated electron systems

The variational local moment approach (VLMA) solution of the single impurity Anderson model is presented. It generalizes the local moment approach of Logan et al. by invoking the variational principle to determine the lengths of local moments and orbital occupancies. We show that VLMA is a comprehensive, conserving and thermodynamically consistent approximation and treats both Fermi and non-Fermi liquid regimes as well as local moment phases on equal footing. We tested VLMA on selected problems. We solved the single- and multi-orbital impurity Anderson model in various regions of parameters, where different types of Kondo effects occur. The application of VLMA as an impurity solver of the dynamical mean-field theory, used to solve the multi-orbital Hubbard model, is also addressed.     

Fast multi-orbital equation of motion impurity solver for dynamical mean field theory

We propose a fast multi-orbital impurity solver for dynamical mean field theory (DMFT). Our DMFT solver is based on the equations of motion (EOMs) for local Green's functions and is constructed by generalizing from the single-orbital case to the multi-orbital case with the inclusion of the inter-orbital hybridizations and applying a mean field approximation to the inter-orbital Coulomb interactions. The two-orbital Hubbard model is studied using this impurity solver within a large range of parameters. The Mott metal-insulator transition and the quasiparticle peak are well described. A comparison of the EOM method with the quantum Monte Carlo method is made for the two-orbital Hubbard model and good agreement is obtained. The developed method hence holds promise as a fast DMFT impurity solver in studies of strongly correlated systems.     

An advanced multi-orbital impurity solver for dynamical mean field theory based on the equation of motion approach

We propose an improved fast multi-orbital impurity solver for the dynamical mean field theory based on equations of motion (EOM) for Green's functions and a decoupling scheme. In this scheme the inter-orbital Coulomb interactions are treated fully self-consistently, and involve the inter-orbital fluctuations. As an example of the use of the derived multi-orbital impurity solver, the two-orbital Hubbard model is studied for various cases. Comparisons are made between numerical results obtained with our EOM scheme and those obtained with quantum Monte Carlo and numerical renormalization group methods. The comparison shows a good agreement, but also reveals a dissimilarity of the behaviors of the densities of states which is caused by inter-site inter-orbital hopping effects and on-site inter-orbital fluctuation effects, thus corroborating the assertion of the value of the EOM method for the study of multi-orbital strongly correlated systems.     

A multi-orbital iterated perturbation theory for model Hamiltonians and real material-specific calculations of correlated systems

The dynamical mean field theory (DMFT) has emerged as one of the most importantframeworks for theoretical investigations of strongly correlated lattice models and realmaterial systems. Within DMFT, a lattice model can be mapped onto the problem of amagnetic impurity embedded in a self-consistently determined bath. The solution of thisimpurity problem is the most challenging step in this framework. The available numericallyexact methods such as quantum Monte Carlo, numerical renormalization group or exactdiagonalization are naturally unbiased and accurate, but are computationally expensive.Thus, approximate methods, based e.g. on diagrammatic perturbation theory have gainedsubstantial importance. Although such methods are not always reliable in various parameterregimes such as in the proximity of phase transitions or for strong coupling, theadvantages they offer, in terms of being computationally inexpensive, with real frequencyoutput at zero and finite temperatures, compensate for their deficiencies and offer aquick, qualitative analysis of the system behavior. In this work, we have developed such amethod, that can be classified as a multi-orbital iterated perturbation theory (MO-IPT) tostudy N-folddegenerate and non degenerate Anderson impurity models. As applications of the solver, wehave embedded the MO-IPT within DMFT and explored lattice models like the single orbitalHubbard model, covalent band insulator and the multi-orbital Hubbard model fordensity-density type interactions in different parameter regimes. The Hund’s couplingeffects in case of multiple orbitals is also studied. The limitations and quality ofresults are gauged through extensive comparison with data from the numerically exactcontinuous time quantum Monte Carlo method (CTQMC). In the case of the single orbitalHubbard model, covalent band insulators and non degenerate multi-orbital Hubbard models,we obtained an excellent agreement between the Matsubara self-energies of MO-IPT andCTQMC. But for the degenerate multi-orbital Hubbard model, we observe that the agreementwith CTQMC results gets better as we move away from particle-hole symmetry. We have alsointegrated MO-IPT+DMFT with density functional theory based electronic structure methodsto study real material systems. As a test case, we have studied the classic, stronglycorrelated electronic material, SrVO₃. A comparison of density of states and photo emissionspectrum (PES) with results obtained from different impurity solvers and experimentsyields good agreement.     

Electronic structure and correlations of vitamin B<Subscript>12</Subscript> studied within the Haldane-Anderson impurity model

We study the electronic structure and correlations of vitamin B₁₂ (cyanocobalamine) by using theframework of the multi-orbital single-impurity Haldane-Anderson model of atransition-metal impurity in a semiconductor host. The parameters of the effectiveHaldane-Anderson model are obtained within the Hartree-Fock (HF) approximation. Thequantum Monte Carlo (QMC) technique is then used to calculate the one-electron andmagnetic correlation functions of this effective model. We observe that new states forminside the semiconductor gap found by HF due to the intra-orbital Coulomb interaction atthe impurity 3d orbitals. In particular, the lowest unoccupiedstates correspond to an impurity bound state, which consists of states from mainly the CNaxial ligand and the corrin ring as well as the Co e_g-like orbitals. We alsoobserve that the Co?(3d) orbitals can develop antiferromagneticcorrelations with the surrounding atoms depending on the filling of the impurity boundstates. In addition, we make comparisons of the HF+QMC data with the density functionaltheory calculations. We also discuss the photoabsorption spectrum of cyanocobalamine.     

Evolution of the electronic structures of NixSiy ordered systems: experimental and theoretical investigations

We study the change of the electronic structures of nickel silicides, Ni₃Si and NiSi₂, as well as nickel and silicon through the evolution of their valence band X-ray photoelectron spectra (v-XPS) both experimentally and theoretically. The experimental spectra are compared to the total and partial densities of states using tight-binding linear muffin-tin orbital method (TB-LMTO) in the atomic sphere approximation (ASA). Good agreement is found between theory and experiment. Received 10 July 2000     

Calculations of localized modes on surface and impurity layer embedded in a semi-infinite Heisenberg ferromagnet

We investigate the magnetic excitations for the magnetic problem arising from the absence of magnetic translation symmetry in one dimension due to the presence of an impurity layer embedded within a semi-infinite ferromagnet. A Heisenberg model is employed to investigate the possibility that localized modes can occur with an impurity layer implanted within a semi-infinite ferromagnet. No electronic effects are considered. The theoretical approach employs the matching procedure in the mean field approximation and determines the propagating and evanescent spin amplitude fields including the contribution due to an applied field. The results are used to calculate the energies of localized modes associated with the impurity layer and with the surface. Numerical examples of the modes are given and they are found to exhibit various effects due to the interplay between the impurity layer and surface modes. It is shown that more localized modes can occur and the modification of the spin wave spectra can be signaled by the appearance of surface and impurity modes, besides the bulk excitations. Also, the bulk spin fluctuations field, the spin waves localized on the surface as well as on impurity layer depend are shown to depend on the nature of the exchange coupling between spin sites, the values of spin sites and the position of the impurity layer from the surface.     

Theoretical study of the time-resolved photoelectron spectrum of Na 2F: effects of thermal initial conditions

The excited state dynamics of the Na₂F cluster initiated by a femtosecond laser pulse is studied considering a thermally excited initial sample. Within a pump-probe set-up, the time-dependent photoelectron spectrum is calculated, which is shown to be a sensitive tool to study intramolecular motion of the cluster. Temperature effects are taken into account through thermal averaging over the time-dependent spectra obtained from different initial vibrational states of the cluster. The nuclear motion upon laser excitation is described by full-dimensional quantum wavepacket propagation using explicit, realistic pump and probe pulses. The characteristic features of the time-resolved photoelectron spectra of the Na₂F cluster, identified as due to periodic bending motion of the cluster as well as to the excitation of the stretching mode, are found to be robust against increasing vibrational temperature of the cluster beam. This finding is important for possible future experiments.     

Elementary excitations for the Anderson model at finite temperatures

The elementary excitation spectrums for the Anderson model at finite temperatures are calculated by using the Bethe-ansatz solution. The formulation is based on the method of Yang and Yang, which was developed for the one-dimensional boson systems with the -function type interaction. We obtain the temperature dependence of the spin and the charge excitation spectrums. When the impurity level lies deeply from the Fermi level and the Coulomb interaction is suitably large, the resonant peak structure develops in the low energy region of the spin excitation spectrum and the hump structure grows around the impurity level of the charge excitation spectrum with decreasing temperature. Received: 21 January 1998 / Accepted: 17 March 1998     

Spectrum of two quasiequal-energy electrons ejected by a high-energy photon

We present numerical results for the photoelectron spectrum in double ionization by keV photons in the quasiequal-energy sharing region. In this region of the spectrum, the relevant ionizing mechanism is due to a mutual sharing of the photon momentum by both electrons, with small momentum transferred to the atomic nucleus. Calculations were performed for photon energies of 25 and 50 keV, where retardation effects are fundamental, while final-state correlations are of minor importance. The spectra present a two-peak structure, with maxima located at the photoelectron energies , with the photon energy in atomic units. We discuss the general features of the spectrum in terms of the picture of the photoionization of two free electrons, and we propose a way of detecting the contribution by experiments. Received 24 January 2000     

Quantum phase transitions in the bosonic single-impurity Anderson model

We consider a quantum impurity model in which a bosonic impurity level is coupled to a non-interacting bosonic bath, with the bosons at the impurity site subject to a local Coulomb repulsion U. Numerical renormalization group calculations for this bosonic single-impurity Anderson model reveal a zero-temperature phase diagram where Mott phases with reduced charge fluctuations are separated from a Bose-Einstein condensed phase by lines of quantum critical points. We discuss possible realizations of this model, such as atomic quantum dots in optical lattices. Furthermore, the bosonic single-impurity Anderson model appears as an effective impurity model in a dynamical mean-field theory of the Bose-Hubbard model.     

Exact solution for a degenerate Anderson impurity in the limit embedded into a correlated host

We consider the one-dimensional t - J model, which consists of electrons with spin S on a lattice with nearest neighbor hopping t constrained by the excluded multiple occupancy of the lattice sites and spin-exchange J between neighboring sites. The model is integrable at the supersymmetric point, J = t. Without spoiling the integrability we introduce an Anderson-like impurity of spin S (degenerate Anderson model in the limit), which interacts with the correlated conduction states of the host. The lattice model is defined by the scattering matrices via the Quantum Inverse Scattering Method. We discuss the general form of the interaction Hamiltonian between the impurity and the itinerant electrons on the lattice and explicitly construct it in the continuum limit. The discrete Bethe ansatz equations diagonalizing the host with impurity are derived, and the thermodynamic Bethe ansatz equations are obtained using the string hypothesis for arbitrary band filling as a function of temperature and external magnetic field. The properties of the impurity depend on one coupling parameter related to the Kondo exchange coupling. The impurity can localize up to one itinerant electron and has in general mixed valent properties. Groundstate properties of the impurity, such as the energy, valence, magnetic susceptibility and the specific heat coefficient, are discussed. In the integer valent limit the model reduces to a Coqblin-Schrieffer impurity. Received: 31 December 1997 / Accepted: 17 March 1998     

Construction and solution of a Wannier-functions based Hamiltonian in the pseudopotential plane-wave framework for strongly correlated materials

Ab initio determination of model Hamiltonian parameters for strongly correlated materials is a key issue in applying many-particle theoretical tools to real narrow-band materials. We propose a selfcontained calculation scheme to construct, with an ab initio approach, and solve such a Hamiltonian. The scheme uses a Wannier-function-basis set, with the Coulomb interaction parameter U obtained specifically for theseWannier functions via constrained Density functional theory (DFT) calculations. The Hamiltonian is solved by Dynamical Mean-Field Theory (DMFT) with the effective impurity problem treated by the Quantum Monte Carlo (QMC) method. Our scheme is based on the pseudopotential plane-wave method, which makes it suitable for developments addressing the challenging problem of crystal structural relaxations and transformations due to correlation effects. We have applied our scheme to the “charge transfer insulator” material nickel oxide and demonstrate a good agreement with the experimental photoemission spectra.     

Theory of resonant inelastic X-ray scattering spectrum for Ni impurities in cuprates

We perform the numerically exact diagonalization calculation for small Cu-O clusters with a Ni impurity site, representing the Ni-substituted cuprate, to examine the single-particle excitation spectra as well as the resonant inelastic X-ray scattering (RIXS) spectra. We clarify relations between low-energy electronic structures near the Ni site and excitations seen in the RIXS spectra.     

Local impurity phase pinning and pinning force in charge density waves

Starting from the static Fukuyama-Lee-Rice equation for a three-dimensional incommensurate charge density wave (CDW) in quasi one-dimensional conductors a solvable model for local phase pinning by impurities is defined and studied. We find that average CDW energy and average pinning force show critical behaviour with respect to the pinning parameter h. Specifically the pinning force exhibits a threshold at h=1 with exponent . Our model exemplifies a general concept of local impurity pinning in which the force exerted by the impurity on the periodic CDW structure becomes multivalued and metastable states appear beyond a threshold. It is found that local impurity pinning becomes less effective at low temperatures and may eventually cease completely. These results are independent of spatial dimensionality as expected for local impurity pinning. Comparison with Larkin's model is also made. Received 8 July 1998     

Laser photoelectron microspectroscopy for imaging impurity ions,color centers,and small-size irregularities in dielectric media

New photoelectron microscopy application fields are considered for imaging the arrangement of color centers, small-size defects, and impurity ions in dielectric matrices. The techniques proposed are based on the first experimental results obtained in studying the possibilities of observing stepwise laser photoelectric effect in ZrO₂:Nd³⁺, where photoelectron emission results from the stepwise absorption of light by the impurity ions Nd³⁺. In that case, the electrons being emitted originate in immediate proximity to the impurity ions, which offers possibilities to image the above structures by photoelectron microscopy techniques.     

Shocks in non-loaded bead chains with impurities

We numerically investigate the problem of the propagation of a shock in an horizontal non-loaded granular chain with a bead interaction force exponent varying from unity to large values. When is close to unity we observed a cross-over between a nonlinearity-dominated regime and a solitonic one, the latest being the final steady state of the propagating wave. In the case of large values of the deformation field given by the numerical simulations is completely different from the one obtained by analytical calculation. In the following we studied the interaction of these shock waves with a mass impurity placed in the bead chain. Two different physical pictures emerge whether we consider a light or a heavy impurity mass. The scatter of the shock wave with a light impurity yields damped oscillations of the impurity which then behave as a solitary wave source. Differently an heavy impurity is just shifted by the shock and the transmitted wave loses its solitonic character being fragmented into waves of decreasing amplitudes. Received 23 June 1999     

Background charges and quantum effects in quantum dots transport spectroscopy

We extend a simple model of a charge trap coupled to a single-electron box to energy ranges and parameters such that it gives new insights and predictions readily observable in many experimental systems. We show that a single background charge is enough to give lines of differential conductance in the stability diagram of the quantum dot, even within undistorted Coulomb diamonds. It also suppresses the current near degeneracy of the impurity charge, and yields negative differential lines far from this degeneracy. We compare this picture to two other accepted explanations for lines in diamonds, based respectively on the excitation spectrum of a quantum dot and on fluctuations of the density-of-states in the contacts. In order to discriminate between these models, we emphasize the specific features related to environmental charge traps. Finally we show that our model accounts very well for all the anomalous features observed in silicon nanowire quantum dots.     

原子势对阈上电离平台的影响

本文从理论上分别研究了长程和短程原子势对阈上电离光电子谱平台结构的影响. 发现在相当大的激光参数范围内, 长程势的阈上电离谱总是呈现出清晰的双平台结构; 对于短程势, 阈上电离谱双平台的界限不再清晰, 随着入射激光强度的减小, 逐渐从双平台过渡到单平台. 基于经典分析和量子力学数值模拟, 阐明了在不同模型势下, 电离速率的差别和再散射电子弹性碰撞截面的不同导致了上述平台结构的差异．此外, 还讨论了激光脉冲空间强度分布对这一现象的影响. 关键词： 阈上电离 离子势影响 中红外激光脉冲