Higher-order Green's Functions Research Articles

Role of Cu d–d inter-orbital electron correlation on the out-of-plane conduction in cuprates

In the present paper we study a model which is relevant to an analysis of the effects of the Cu d–d inter-orbital electron correlation on the motion of charge carriers along c-axis in high- T c cuprates. For this a microscopic model Hamiltonian for the three atom cluster CuO 2 which incorporates the essential features of the basic unit of high- T c cuprates has been considered. The model Hamiltonian for this three atom cluster includes various in-plane and out-of-plane orbital energies, their intra- and inter-orbital Coulomb interactions relevant for the electrons in the cluster. The out-of-plane correlation which appears when we consider the hopping of a hole from the Cu 3d 3 z 2− r 2 to apical O 2p z orbitals has been calculated using the Green's function technique. The equation of motion for the relevant Green's function contains higher order Green's functions and we evaluate the correlation parameter relevant to motion for a hole along the c-axis by using suitable decoupling approximations. It has been found through numerical calculations that the out-of-plane correlations depend on the intra- and inter-orbital Coulomb interactions, the out-of-plane orbital energies, hole occupancy and on temperature. Finally, the relevance of the out-of-plane correlation parameter for present three atom CuO 2 cluster model to the c-axis conductivity of the bulk high- T c cuprate systems has been pointed out.

New approach to electromagnetic wave tails on a curved spacetime

We present an alternative method for constructing the exact and approximate solutions of electromagnetic wave equations whose source terms are arbitrary order multipoles on a curved spacetime. The developed method is based on the higher-order Green's functions for wave equations which are defined as distributions that satisfy wave equations with the corresponding order covariant derivatives of the Dirac delta function as the source terms. The constructed solution is applied to the study of various geometric effects on the generation and propagation of electromagnetic wave tails to first order in the Riemann tensor. Generally the received radiation tail occurs after a time delay which represents geometrical backscattering by the central gravitational source. It is shown that the truly nonlocal wave-propagation correction (the tail term) takes a universal form which is independent of multipole order. In a particular case, if the radiation pulse is generated by the source during a finite time interval, the tail term after the primary pulse is entirely determined by the energy-momentum vector of the gravitational field source: the form of the tail term is independent of the multipole structure of the gravitational source. We apply the results to a compact binary system and conclude that under certain conditions the tail energy can be a noticeable fraction of the primary pulse energy. We argue that the wave tails should be carefully considered in energy calculations of such systems.

Electromagnetic wave tails on curved spacetime and their observational implications

We calculate the tail term of the electromagnetic potential of a pulsed source in arbitrary bounded motion in a weak gravitational field using a higher-order Green's function approach and demonstrate that generally the received radiation tail arrives after a time delay which represents geometrical backscattering by the central gravitational source. We apply the results to a compact binary system and conclude that under certain conditions the tail energy can be a noticeable fraction of the direct pulse energy.

Moment-conserving decoupling approach for many-body systems

A nonperturbative, controllable, and moment-conserving decoupling approach is proposed. Our assumption is that a higher-order Green function (GF) essentially contains two-part information. One part relates to the single-particle GF, which is involved in the corresponding moment; the other part is a higher-order quantity, which is independent of the single-particle GF. Thus the higher-order GF may be separated into two corresponding terms. We derive the chain of equations of motion (EOM) of the latter term from the usual EOM for GF's. To solve the equations a truncation approximation is made at the level desired. The single-band Hubbard model is studied using this approach. Moment-conserving solutions up to the order $m=2$ are obtained. The properties of a solution corresponding to the Hubbard-I approximation level are discussed in detail. The quasiparticle bands and the momentum distribution are in excellent agreement with the results from the quantum Monte Carlo simulation.

Role of interlayer interactions on transition temperature in high- Tc cuprate superconductors

The effect of interlayer interactions on transition temperature in high- T c layered superconductors has been studied using a one-band two-layer tight binding Hamiltonian with intra- and interlayer attractive interactions. The double-time Green's function technique is employed and higher-order Green's functions are linearized by using a mean field decoupling approximation. The expressions for the transition temperature ( T c) and excitonic type interlayer correlation ( γ c) are obtained. It is shown that interlayer interactions play an important role in the enhancement of T c in high- T c cuprates. We have also explained the relevance of our results in high- T c layered superconductors having two layers per unit cell under externally applied pressure.

Method for breaking chains of equations for green's functions

This article presents a new method for closing infinite systems of equations for Green's functions. Its basis is a procedure for simultaneously splitting two higher-order Green's functions. There is a particular relationship between the three Green's functions that result. These Green's functions are self-consistent. Known Green's functions are used to reconstruct the corresponding correlation functions. An example is provided by the problem of magnetization for a spin system in the Heisenberg model with first-and secondorder approximations in the spin-spin interaction. The first-order approximation corresponds to the molecular-field approximation. The second-order computation corresponds to obtaining general relations determining the magnetization of a system.

Equation-of-motion treatment of the impurity Anderson model with a finite on-site Coulomb repulsion.

The impurity Anderson model with a finite Coulomb repulsion U has been studied by using the conventional equation-of-motion treatment for the f-electron Green's function. To get a closed equation, two types of approximations are incorporated. One is to neglect, in a large U limit, higher order Green's functions which involve three f-electron annihilation operators. The other is to linearize the equation of motion by using a projection operator method. The average valency ${\mathit{n}}_{\mathit{f}}$ and the spectral density of states (DOS) of f electrons are evaluated from the self-consistent equation for the Green's function. Results for ${\mathit{n}}_{\mathit{f}}$ are in good agreement with exact results of Bethe ansatz method, and the obtained spectral DOS exhibits a well-known three-peak structure. Effects of finite U and finite temperature on the spectral DOS are discussed.

Chemisorption at finite coverages—the coherent potential approximation vs the equation of motion for green's functions method

The electronic structure, chemisorption energy and adatom charge of the chemisorbed overlayer on a metal surface are studied within the model by the Newns Hamiltonian generalized to finite coverages. It is shown that the method of equation of motion for appropriate Green's function together with some decouplings of the higher-order Green's functions can be used in calculations of the overlayer's electronic properties as an efficient and alternative way to the coherent potential approximation method.

Green's Function Theory of the Two-Dimensional Ising Model –Derivation of the Logarithmic Divergence of the Specific Heat–

The S =1/2 Ising model for a square lattice is studied by means of the two-time Green's function method. A simple assumption is introduced associating with the rigorous relations among several spin correlation functions which are derived by this method and any approximations such as decoupling ones for the higher order Green's functions are not used. The specific heat obtained by using this assumption shows the logarithmic divergence just below and just above T c . It is ascertained that the theory issues only the error of order 1/ T 4 in the sum rule and in the susceptibility in the high temperature region.

Nonstandard formulation of perturbation theory for Green's function

Perturbation theory is developed for two-variable Green's functions (GF) when the initial GF is linked simultaneously to several higher-order GF. The total mass operator of the initial GF is obtained mathematically correctly in a form convenient for use. As an example of the application of this method, the mass operator of a nuclear spin anticommutator GF is calculated.

Magnetically induced structural phase transitions

We consider the multiple spin density wave states of an itinerant model of a face centred cubic antiferromagnet. By investigating the total energies in the Hartree-Fock approximation and the susceptibility and higher order Green's functions in the random phase approximation we examine the transitions between the various MSDW phases. We show that for a special type of phase transition in which the spin components reorientate themselves we can have softening of phonons and the corresponding shear elastic constant in agreement with existing experiments. We suggest further experimental verification of our model.

Transport properties of spin-glasses. Effect of including Kondo-like terms

Transport properties in spin-glasses have been studied for the $s\ensuremath{-}d$ model using the method of the double-time Green's function. The higher-order Green's functions have been decoupled to lower orders using Nagaoka's decoupling scheme. The self-energy has been obtained in a multiple-scattering approximation. A self-consistent expression for the $t$ matrix has been obtained using Hamann's approach, and the temperature ${T}_{m}$, at which the resistivity is maximum, has been calculated. An expression for the Lorenz number has been obtained, following the procedure of Nam and Fullenbaum. The relative contribution to the Lorenz number ($\frac{\ensuremath{\Delta}L}{{L}_{0}}$), where $L$ is the contribution to the Lorenz number due to the exchange interaction $J$, is lower in the spin-glass system as compared to the Kondo system. The thermoelectric power has been calculated using the perturbation expansion of the self-energy to order ${J}^{3}$. It is found to contain values ${V}_{0}{J}^{2}$ and ${V}_{0}{J}^{3}$, where the second term is very large and dominates over the first term at low temperature, and the sign of the thermoelectric power is therefore decided by the sign of ${V}_{0}$ and $J$. The thermoelectric power involves a term such as $Q+\ensuremath{\chi}$, where $Q$ is the spin-glass order parameter and $\ensuremath{\chi}$ is the spin-deviation correlation function. No abrupt change in the calculation of the thermoelectric power is found around ${T}_{f}$, which is supported by the experimental data. The thermoelectric power calculation agrees well with the experimental data at low temperatures but there is a systematic discrepancy between the two at high temperatures due to the neglect of the electron-phonon interaction in the present calculation.

Unified first-order Green's-function theory of anisotropic Heisenberg ferromagnets forS=12

A unified first-order Green's-function theory of anisotropic Heisenberg ferromagnets with $S=\frac{1}{2}$ is designed to decouple the higher-order Green's functions obtained in writing down the equations of motion of the first-order Green's functions. By defining the commutator and the anticommutator brackets, the equations of motion of the two kinds of Green's functions ${G}^{\ensuremath{-}}$ and ${G}^{+}$ are written down. With the use of suitable decoupling parameters, a generalized decoupling scheme is suggested. In order to determine the relation between these decoupling parameters we define two conditions: (1) self-consistency and (2) vanishing of the equal-time correlation functions. Using this decoupling scheme, we calculate the thermodynamic properties of the anisotropic Heisenberg ferromagnets with $S=\frac{1}{2}$ at low temperatures. Finally, we also calculate the effect of the decoupling scheme on the magnon conductivity at low temperatures. We clearly find that the magnon conductivity is modified appreciably by the different decoupling parameters and by the anisotropy of the system.

Effects of biquadratic exchange interaction on dynamic susceptibility in Heisenberg ferromagnet

The Green function technique has been employed to study the dynamic susceptibility of a spin-1 system above the Curie temperature. Bilinear and biquadratic terms have been added in writing the Hamiltonian of the system. Higher order Green functions have been decoupled by RPA and Callen type decouplings. The dependence of spin wave energy, intensity and susceptibility on wavevector and biquadratic parameter have been studied.

Transverse magnetoresistance in spin-glass alloys

The scattering of the conduction electrons by magnetic ions in the spin-glass phase in the presence of a magnetic field has been investigated. The transverse magnetoresistance of spinglasses has been calculated using the method of the double-time Green's function and the Kubo-Greenwood formula. The higher-order Green's functions have been decoupled into the lower-order Green's functions using Nagaoka's decoupling approximation. In the first approximation we have neglected the correlation function describing the quasibound states between the conduction electron and the impurity spin. The self-energy of the Green's function has been obtained to the second order in normal and exchange interactions ${V}_{0}$ and $J$, respectively. It is found that the self-energy consists of two parts: one involving the spin-glass order parameter $Q$ and the other spin-deviation correlation function. An expression for the transverse magnetoresistance has been obtained by evaluating the relaxation time at the Fermi surface.

Second-order Green's-function approach for the study of the sensitivity of the Curie temperature to single-ion anisotropy

This paper utilizes the second-order Green's-function formalism to treat a Heisenberg ferromagnet in the presence of single-ion crystal-field anisotropy represented by the Hamiltonian: $H=\ensuremath{-}J\ensuremath{\Sigma}{i,\ensuremath{\delta}}^{}({\stackrel{\ensuremath{\rightarrow}}{\mathrm{S}}}_{i}\ifmmode\cdot\else\textperiodcentered\fi{}{\stackrel{\ensuremath{\rightarrow}}{\mathrm{S}}}_{i+\ensuremath{\delta}})\ensuremath{-}D\ensuremath{\Sigma}{i}^{}{({S}_{i}^{z})}^{2}$. Second-order equations of motion for the Green's functions $〈〈{S}_{i}^{z}; {S}_{j}^{z}〉〉$ and $〈〈{{S}_{i}}^{+}; {{S}_{j}}^{\ensuremath{-}}〉〉$ are developed and the higher-order Green's functions are decoupled in the zeroth-order approximation in which the interspin correlations are not taken into account rigorously. The spin-correlation functions are derived and are solved self-consistently in the limit of zero spontaneous magnetization. The Curie temperature is thus obtained. Calculations are restricted to a simple-cubic lattice and positive values of $D$ only, and the sensitivity of the Curie temperature to the single-ion anisotropy is critically examined for a spin-1 lattice. It is seen that the results agree very closely with those of the Green's-function diagram technique. The results are also compared with those of the first-order Green's-function theory using the random-phase approximations of Lines using the correlated-effective-field approximation, and of the molecular-field theory.

Spin-wave renormalization in the Heisenberg ferromagnet. III.S>~1

The work reported in two earlier papers is completed, with the derivation of a fully consistent first-order Green function theory of the Heisenberg ferromagnet for the case $Sg~1$. The equal-time correlation-function (ETCF) relations that follow from the decoupling of higher-order Green functions help derive a unique and consistent decorrelation scheme appropriate to the problem. Both the Dyson-Maleev boson-operator representation and the original spin-operator representation are considered. The rigorous low-temperature results of Dyson for both the spontaneous magnetization and the internal energy are correctly reproduced in the simple theory deduced. Callen's decoupling is shown to be an approximation to the actual, consistent scheme in the low $T$, large $S$ case. Some brief concluding remarks summarize certain results on decoupling in general that have been gleaned from the three papers of this series.

An X-Y antiferromagnet

A two-sublattice X-Y antiferromagnet is treated using the second-order Green function theory. The higher-order Green functions are decoupled by the random phase approximation (RPA), and the transition temperature T N, where the paramagnetic staggered susceptibility diverges, and the critical values of the spin correlation functions are calculated for systems having simple cubic and body centred cubic lattice structures and for all spin values. Comparing the results with the experimental Néel temperatures of Co(C 5H 5NO) 6(ClO 4) 2 and Co(C 5H 5NO) 6(BF 4) 2 we get J/ k B=0.258 K and 0.216 K for these compounds, respectively.

Nonsteady perturbation theory for Green's functions

A simple method is proposed for uncoupling a complex chain of Green's function (GF) equations when the initial GF is coupled simultaneously with several higher-order GF. Uncoupling of the chain of equations of motion for the nuclear spin anticommutator Green's function provides an example of the use of this method.

A Heisenberg antiferromagnet using second-order Green function theory

A two-sublattice Heisenberg antiferromagnet is treated using the second-order Green function formalism. The higher order Green functions are decoupled according to the random-phase approximations and the transition temperatures TN, where the paramagnetic staggered susceptibility diverges, and the nearest-neighbour correlation functions are calculated for systems having simple cubic and body centred cubic lattice structures and spin 1/2 to 7/2.