Spectral function and self-energy of the one-dimensional Hubbard model in the U →∞ limit

The interpretation of the k dependent spectral functions of the one-dimensional, infinite U Hubbard model obtained by using the factorized wave-function of Ogata and Shiba is revisited. The well defined feature which appears in addition to low energy features typical of Luttinger liquids, and which, close to the Fermi energy, can be interpreted as the shadow band resulting from 2k _F spin fluctuations, is further investigated. A calculation of the self-energy shows that, not too close to the Fermi energy, this feature corresponds to a band, i.e. to a solution of the Dyson equation ω-ε(k)-ReΣ(k,ω) = 0.     

Second-order optical nonlinearities from χ gratings induced by holographic all-optical poling

The paper presents the second-order optical nonlinearities from χ⁽²⁾ gratings induced by holographic all-optical poling for azobenzene polymer. Second harmonic (SH) signal along the directions with two different vectors was measured. One is strong SH signal diffracted in the same direction as 2ω writing beam with wave vector k_2ω and the other is weak SH signal diffracted in the direction of wave vector of 4k_ω - k_2ω + Δk where k_ω is wave vector of ω beam and Δk is the wave vector mismatch whose vector is parallel to k_ω. The latter signal was used as a tool to monitor the formation of holographic χ⁽²⁾ gratings in real-time because it has off-axis wave vector different from both k_ω and k_2ω. The increase of 2ω intensity on poling process led to the large increase of second-order optical nonlinearity. The real-time monitoring showed that it also gave the large relaxation of second-order optical nonlinearity on poling process. The increase of 2ω (532 nm) energy enhanced the increase of local heating, which led to easier alignment of azobenzene chromophore and also larger relaxation of aligned chromophore.     

Comparative study of electron- and hole-doped high-Tc compounds in pseudogap regime: LDA+DMFT+Σk approach

Pseudogap regime for the prototype high-T_c compounds hole-doped Bi₂Sr₂CaCu₂O_8−x (Bi2212) and electron-doped Nd_2−xCe_xCuO₄ (NCCO) is described by means of novel generalized LDA+DMFT+Σ_k approach. Here, conventional dynamical mean-field theory (DMFT) equations are supplied with additional (momentum dependent) self-energy Σ_k. In the present case, Σ_k describes nonlocal dynamical correlations induced by short-ranged collective Heisenberg-like antiferromagnetic spin fluctuations. Material-specific model parameters of two neighboring CuO₂ layers of Bi2212 and single CuO₂ layer of NCCO were obtained within local density approximation (LDA) and constrained LDA method. We show that Fermi surface in presence of the pseudogap fluctuations have perfectly visible “hot-spots” for NCCO, while in Bi2212 there is just a rather broad region with strong antiferromagnetic scattering. Results obtained are in good agreement with recent ARPES and optical experiments.     

Destruction of the Fermi surface due to pseudogap fluctuations in strongly correlated systems

We generalize the dynamical-mean field theory (DMFT) by including into the DMFT equations dependence on the correlation length of the pseudogap fluctuations via the additional (momentum dependent) self-energy Σ_k. This self-energy describes nonlocal dynamical correlations induced by short-ranged collective SDW-like antiferromagnetic spin (or CDW-like charge) fluctuations. At high enough temperatures, these fluctuations can be viewed as a quenched Gaussian random field with finite correlation length. This generalized DMFT + Σ_k approach is used for the numerical solution of the weakly doped one-band Hubbard model with repulsive Coulomb interaction on a square lattice with nearest and next nearest neighbor hopping. The effective single impurity problem is solved by using a numerical renormalization group (NRG). Both types of strongly correlated metals, namely, (i) doped Mott insulator and (ii) the case of the bandwidth W ? U (U-value of local Coulomb interaction) are considered. By calculating profiles of the spectral densities for different parameters of the model, we demonstrate the qualitative picture of Fermi surface destruction and formation of Fermi arcs due to pseudogap fluctuations in qualitative agreement with the ARPES experiments. Blurring of the Fermi surface is enhanced with the growth of the Coulomb interaction.     

Second order self-energy of the two-dimensional Hubbard model

The self-energy Σ(k; ω) of the 2D Hubbard model on the square lattice is calculated numerically in second order perturbation theory. In the limit of small frequencies the imaginary part of Σ(k; ω) is also obtained analytically. We find that at half filling ImΣ(k; ω) ～ ω for k on the Fermi surface, with a logarithmically divergent prefactor close to the corners k = (0,±π) and (±π,0) in agreement with the numerical results.     

Self-consistent calculation of the optical potential and ground-state properties of nuclear matter

On the basis of the Green-function formalism, we performed a self-consistent calculation of the self-energy ∑(k, ω) of a particle interacting with the infinite nuclear medium. The function ∑(k, ω) was mapped out in the energy-momentum plane, and the single-particle energy ω(k), momentum distribution ?(k) and the “on-shell” part of the self-energy, ∑(k, ω(k)), were defined, from which all physical properties followed. In particular we investigated the ground-state properties of nuclear matter in two Λ-approximations of the T-matrix. In one, the intermediate two-particle propagator, Λ₀₀, represented free-particle propagation; in the other, called Λ₁₁, intermediate states included both interacting particles and holes. Pauli principle effects were included in both approximations. The second approximation was expected to be conserving because it included a large part of the rearrangement effects which, we found, contributed ～6 MeV per particle to the average energy and ～28 MeV to the singleparticle energy at zero momentum. The Hugenholtz-van Hove theorem was nearly satisfied, with only 1 MeV separating the chemical potential from the average energy. We also studied, in the Λ₀₀-approximation, the optical potential for the scattering of a particle by a large nucleus; it was directly related to the “on-shell” part of the self-energy. It was found that, below 100 MeV, the real part varied as (?90 + 0.584E) [MeV], and the imaginary part as (2.4 + 0.009 E) [MeV].     

ARPES spectral functions and Fermi surface for La<Subscript>1.86</Subscript>Sr<Subscript>0.14</Subscript>CuO<Subscript>4</Subscript> compared with LDA + DMFT + Σ<Subscript>k</Subscript> calculations

The slightly underdoped high-temperature system La_1.86Sr_0.14CuO₄ (LSCO) is studied by means of high-energy high-resolution angular resolved photoemission spectroscopy (ARPES) and the combined LDA + DMFT + Σ _k computational scheme. The corresponding one-band Hubbard model is solved via dynamical mean field theory (DMFT), and the model parameters needed are obtained from first principles in the local density approximation (LDA). An “external” k-dependent self-energy Σ _k describes the interaction of correlated electrons with antiferromagnetic (AFM) pseudogap fluctuations. Experimental and theoretical data clearly show a “destruction” of the LSCO Fermi surface in the vicinity of the (π, 0) point and formation of “Fermi arcs” in the nodal directions. ARPES energy distribution curves as well as momentum distribution curves demonstrate a deviation of the quasiparticle band from the Fermi level around the (π, 0) point. The same behavior of spectral functions follows from theoretical calculations suggesting the AFM origin of the pseudogap state.     

Optical conductivity in the t − J model

Frequency dependent conductivity σ(ω) is calculated for the t ? J model by applying the memory function technique in terms of the Hubbard operators. The relaxation rate due to electron scattering on spin and charge dynamical fluctuations is calculated and a generalized Drude law for σ(ω) is obtained. For a model with an incoherent spectrum for one-hole excitations we obtain a universal form for frequency dependence of relaxation rate and conductivity in terms of the scaling function γ(ω/kT). The relaxation rate for the t ? J model is quite different from that one for the conventional Hubbard model in the strong coupling limit where it vanishes due to an exact cancellation of the intraband scattering and virtual interband transitions.     

Superconducting properties of the attractive Hubbard model

A self-consistent set of equations for the one-electron self-energy in the ladder approximation is derived for the attractive Hubbard model in the superconducting state. The equations provide an extension of a T-matrix formalism recently used to study the effect of electron correlations on normal-state properties. An approximation to the set of equations is solved numerically in the intermediate coupling regime, and the one-particle spectral functions are found to have four peaks. This feature is traced back to a peak in the self-energy, which is related to the formation of real-space bound states. For comparison we extend the moment approach to the superconducting state and discuss the crossover from the weak (BCS) to the intermediate coupling regime from the perspective of single-particle spectral densities.     

Theory of the local field correction in an electron gas

The wave-vector- and frequency-dependent dielectric function ?(k,ω) of an electron gas can be expressed in terms of Lindhard's function and a complex local field correctionG(k,ω) which incorporates all the effects of dynamic exchange and correlation in the system. The general properties ofG(k,ω) are discussed, in particular the static and high-frequency limits. It is shown that for smallk, bothG(k, 0) andG(k, ∞) vary ask ², with different coefficients, but both determined by the average kinetic and potential energies per particle. For largek,G(k, ∞) varies again ask ² and it is argued that the same holds true forG(k, 0), with both coefficients (though different) determined by the average kinetic energy per particle. General formulas for the plasma dispersion relation and damping, involving, respectively, the real and imaginary parts ofG(k,ω), are given. The term in the plasma frequency which is proportional tok ² is given directly in terms of the average kinetic and potential energies per particle, a result true at all temperatures. A calculation of the frequency dependence ofG(k,ω), starting from the exact equation of motion for the particle-hole operator and employing a decoupling approximation introduced previously by Toigo and Woodruff, is presented. Explicit results forG(k,ω) are obtained for smallk and allω. The complete expressions forG(k, 0) andG(k, ∞) in this approximation have been obtained and are plotted.     

Breakdown of Luttinger's theorem in two-orbital Mott insulators

An analysis of Luttinger's theorem shows that – contrary to recent claims – it is not valid for a generic Mott insulator. For a two-orbital Hubbard model with two electrons per site the crossover from a non-magnetic correlated insulating phase (Mott or Kondo insulator) to a band insulator is investigated. Mott insulating phases are characterized by poles of the self-energy and corresponding zeros in the Greens functions defining a “Luttinger surface” which is absent for band insulators. Nevertheless, the ground states of such insulators with two electrons per unit cell are adiabatically connected.     

Eliashberg analysis of tunneling experiments: support for the pairing glue hypothesis in cuprate superconductors

Evidence for the validity of the pairing glue interpretation of high temperature superconductivity is presented using a modified Eliashberg analysis of experimental superconductor-insulator-superconductor (SIS) tunneling data in B2Sr2CaCu2O8 (Bi2212) over a wide range of doping. This is accomplished by extracting detailed information on the diagonal and anomalous contributions to the quasiparticle self-energy. In particular, a comparison of the imaginary part of the anomalous self-energy ImΦ(ω) and the pairing glue spectral function α2F(ω) used in the model is consistent with Hubbard model simulations in the literature. In addition, the real part of the diagonal self-energy for optimal doped Bi2212 bears a strong resemblance to that obtained from photoemission experiments.     

Active suppression of narrowband noises in 3D sound fields

This paper presents a simple multiple-input-multiple-output (MIMO) controller for active suppression of narrowband noise in 3D sound fields. The controller only depends on a complex matrix H(jω₀) instead of an n × n transfer matrix to model the secondary paths. Unlike other available ANCs that obtain the controller transfer functions by adaptation, the proposed one solves its controller transfer matrix directly from H(jω₀); and tolerates some degrees of errors in H(jω₀). If necessary, the proposed system may be made adaptive to trace the drifting secondary path. Online identification of a matrix H(jω₀) is easier than that of a transfer matrix with many coefficient matrices. The estimate would be more accurate for H(jω₀) if other conditions remain the same. The proposed scheme can be modified to suppress narrowband noises with multiple bands by a moderate increase in complexity.     

TOWARDS DEEP AND SIMPLE UNDERSTANDING OF THE TRANSCENDENTAL EIGENPROBLEM OF STRUCTURAL VIBRATIONS

When using exact methods for undamped free vibration problems the generalized linear eigenvalue problem (K−ω²M) D=0 of approximate methods, e.g., finite elements, is replaced by the transcendental eigenvalue problem K (ω) D=0. Here ω is the circular frequency; D is the displacement amplitude vector; M and K are the mass and static stiffness matrices; and K (ω) is the dynamic stiffness matrix, with coefficients which include trigonometric and hyperbolic functions involving ω and mass because elements (for example, bars or beams) are analyzed exactly by solving their governing differential equations. The natural frequencies of this transcendental eigenvalue problem are generally found by the Wittrick-Williams algorithm which gives the number of natural frequencies below ω_t, a trial value of ω, as ∑J_m+s{K (ω_t)} wheres {} denotes the readily computed sign count property of K (ω) and the summation is over the clamped-clamped natural frequencies of all elements of the structure. Understanding the alternative solution forms of the transcendental eigenvalue problem is important both to accelerate convergence to natural frequencies, e.g., by plotting ∣K (ω)∣, and to improve the mode calculations, which lack the complete reliability of natural frequencies obtained by using the Wittrick-Williams algorithm. The three solution forms are: ∣K (ω)∣=0; D=0 with ∣K (ω)∣→∞; and ∣K (ω)∣≠0 with D≠0. The literature covers the first two forms thoroughly but the third form has been almost totally ignored. Therefore, it is now examined thoroughly, principally by analytical studies of simple bar structures and also by confirmatory numerical results for a rigidly jointed plane frame. Although structures are unlikely to have exactly the properties giving this form, it needs to be understood, particularly because ill-conditioning can occur for structures approximating those for which it occurs.     

Electron Green's function in the planar t − J model

The electron Green's functions G(k, ω) within the t ? J model and in the regime of intermediate doping is studied analytically using equations of motion for projected fermionic operators and the decoupling of the self energy into the single-particle and spin fluctuations. It is shown that the assumption of marginal spin dynamics at T = 0 leads to an anomalous quasiparticle damping. Numerical results show also a pronounced asymmetry between the hole (ω < 0) and the electron (ω > 0) part of the spectral function, whereby hole-like quasiparticles are generally overdamped.     

Matrix element and strong electron correlation effects in ARPES from cuprates

We discuss selected results from our recent work concerning the angle-resolved photoemission (ARPES) spectra from the cuprates. Our focus is on developing an understanding of the effects of the ARPES matrix element and those of strong electron correlations in analyzing photointensities. With simulations on Bi₂Sr₂CaCu₂O_8+δ (Bi2212), we show that the ARPES matrix element possesses remarkable selectivity properties, such that by tuning the photon energy and polarization, emission from the bonding or the antibonding states can be enhanced. Moreover, at low photon energies (below 25 eV), the Fermi surface (FS) emission is dominated by transitions from just the O-atoms in the CuO₂ planes. In connection with strong correlation effects, we consider the evolution with doping of the FS of Nd_2−xCe_xCuO_4±δ (NCCO) in terms of the t−t′−U Hubbard model Hamiltonian. We thus delineate how the FS evolves on electron doping from the insulating state in NCCO. The Mott pseudogap is found to collapse around optimal doping suggesting the existence of an associated quantum critical point.     

Quasiparticle lifetime in graphite studied by ultrahigh-resolution ARPES

We have performed ultrahigh-resolution angle-resolved photoemission spectroscopy (ARPES) to elucidate the nature of quasiparticle dynamics in graphite. We found fairly sharp quasiparticle peak of π band around K(H) point in the vicinity of the Fermi level, together with the strong mass renormalization of the band (kink). The imaginary part of electron self-energy (ImΣ) shows a sudden drop below 0.18 eV, indicative of a strong electron-phonon coupling. The linear energy dependence of ImΣ at higher binding energies provides an evidence for the deviation from the conventional Fermi liquid theory.     

On the theory of superconductivity in the extended Hubbard model

A microscopic theory of superconductivity in the extended Hubbard model which takes into account the intersite Coulomb repulsion and electron-phonon interaction is developed in the limit of strong correlations. The Dyson equation for normal and pair Green functions expressed in terms of the Hubbard operators is derived. The self-energy is obtained in the noncrossing approximation. In the normal state, antiferromagnetic short-range correlations result in the electronic spectrum with a narrow bandwidth. We calculate superconducting T _c by taking into account the pairing mediated by charge and spin fluctuations and phonons. We found the d-wave pairing with high-T _c mediated by spin fluctuations induced by the strong kinematic interaction for the Hubbard operators. Contributions to the d-wave pairing coming from the intersite Coulomb repulsion and phonons turned out to be small.     

Zero frequency dynamical structure factor of liquids

Expressions for the zero frequency dynamical structure factor, S(k, ω = 0), are derived from the theory of collective motion of liquids proposed by the authors and that by Hubbard and Beeby. Calculations on liquid argon show that in comparison with the latter, the former theory gives much higher values of S(k, 0) which are in good agreement with the recent experimental results.     

Tuning the dispersion of 4f bands in the heavy-fermion material YbRh2Si2

Localized Yb 4f and itinerant Rh 4d states are subject to substantial hybridization effects in the heavy-fermion material YbRh₂Si₂. The proximity to the Fermi level and the high anisotropy in k space naturally raise questions regarding the role of these hybridization effects for the observed, unusual physical properties. Using angle-resolved photoemission spectroscopy (ARPES) we found that the non-dispersive behavior of the localized Yb f states is broken around the Γ point due to interaction with approaching Rh 4d bands. The intriguing point here is that the hybridization strength turns out to be systematically tunable by electron doping of the material. Gradual deposition of silver atoms onto the atomically clean, silicon terminated surface of YbRh₂Si₂ leads to transfer of Ag 5s charge into the Rh 4d bands. This substantially changes the energy overlap, and thus the hybridization strength, between the interacting Yb 4f and Rh 4d bands in the surface and subsurface region. The shown possibility to control the variation of the f-d hybridization at the surface of heavy-fermion materials may also be helpful for other ARPES studies on the diverse phenomena in electron-correlated materials.