On the theory of localization in disordered systems

A localization criterion is derived by using the self-consistent determination of the self-energy in the discussion of the convergence of the Green function renormalized perturbation expansion. This criterion depends on the dimensionality and the connectivity of the lattice. It yields localization for all states in one-dimension systems and tends to the Economon-Cohen criterion when the number of neighbours tends to infinity. Moreover, one can show that delocalization occurs when the width of the probability distribution of the self-energy is of the order of magnitude of the hopping integral.     

New approach to perturbation theory of many-particle systems

We derive an infinite hierarchy of integral equations for the Green functions of a many-particle system. This set of equations forms the basis of a unified approach to the perturbation theory of many boson and many fermion systems and avoids the introduction of the adiabatic hypothesis. It is demonstrated how a well-known ground state perturbation theory of a system of interacting fermions is obtained without introducing disconnected diagrams. It is shown that the formalism allows a self-consistent determination of the condensate Green function of a condensed Bose system and a derivation of the Beliaev, Hugenholtz, and Pines result for the single-particle k 0 Green function is given. A new self-consistent equation for the k = 0 Green function is solved to yield the well-known self-energy relation ₁₁ – ₀₂ = which plays the role of a self-consistency condition on the theory.     

Single-site theory for the random Hubbard alloy

A new theory for the random system with electron correlation is presented, which is an extension of the Hubbard's theory for the random system and also an extension of the CPA for the interacting electron system. The equation of motion for the Green function is solved by the same decoupling method used by Hubbard. The self-consistent relations for the Green function, the self-energy and the effective occupation number are derived. It is predicted in the binary alloy system that tails or satellites of the state density are produced by the combined effect of the randomness and electron correlation. The origin of the tail is the inelastic scattering of the electron byA — B atomic pairs, whose electronic configuration is changed during the scattering. Numerical calculations are reported for a simple model.     

One-Particle Spectral Function of Electrons in a Hot and Dense Plasma

A self-consistent determination of the spectral function and the self-energy of electrons in a hot and dense plasma is reported. The self-energy is determined within the approximation of the screened potential (GW approximation). The rigorous self-consistent calculation of the spectral function is compared with the quasi-particle approximation. Results are presented for the solar core plasma as well as for ICF plasmas. It is shown, that the quasi-particle concept is not an adequate concept for these plasmas. For the sake of comparison an effective quasi-particle picture is introduced.     

Saturation of nuclear matter and realistic interactions

In this communication we study symmetric nuclear matter for the Brueckner-Hartree-Fock approach, using two realistic nucleon-nucleon interactions (CD-Bonn and Bonn C). The single-particle energy is calculated self-consistently from the real on-shell self-energy. The relation between different expressions for the pressure is studied in cold nuclear matter. For best calculations the self-energy is calculated with the inclusion of hole-hole (hh) propagation. The effects of hh contributions and a self-consistent treatment within the framework of the Green function approach are investigated. Using two different methods, namely, G-matrix and bare potential, the hh term is calculated. We found that using G-matrix brought about non-negligible contribution to the self-energy, but this difference is very small and can be ignored if compared with the large contribution coming from particle-particle term. The contribution of the hh term leads to a repulsive contribution to the Fermi energy which increases with density. For extended Brueckner-Hartree-Fock approach the Fermi energy at the saturation point fulfills the Hugenholtz-Van Hove relation.     

Ward identity and effective medium approximation for conductivity of liquid metals

The self-energy to define the ensemble average of a one-electron Green function for a disordered system is related to the vertex correction for the average of the product of two Green functions by the generalized optical theorem or by the so-called Ward identity. Using this relationship, we evaluate the conductivity of liquid metals both by the Ishida-Yomezawa approximation and by the effective medium approximation from the self-energy forms corresponding to respective approximations. The conductivity formulations thus obtained are shown to be identical with those derived from the diagram method.     

Modifications of single-particle properties in nuclear matter induced by three-body forces

Within the self-consistent Green’s function formalism, we study the effects of three-body forces on the in-medium spectral function, self-energy and effective mass of the nuclear matter constituents, analyzing the density and momentum dependence.     

Dyson equation for Heisenberg ferromagnet

An exact representation for the self-energy operator of the two-time Green function for the transverse spin components for the Heisenberg ferromagnet is obtained.     

Effect of temperature on phonon contribution to Green function of high-temperature superconducting cuprates

The phonon contribution to the nodal electron Green function in cuprates is considered. It is shown that the temperature dependence of the real part of the self-energy component of the Green function for cuprates with a hole doping level close to optimal is described by the electron-phonon interaction in the framework of the extended Eliashberg model.     

Magnetism in the single-band Hubbard model

A self-consistent spectral density approach (SDA) is applied to the Hubbard model to investigate the possibility of spontaneous ferro- and antiferromagnetism. The starting point is a two-pole ansatz for the single-electron spectral density, the free parameter of which can be interpreted as energies and spectral weights of respective quasiparticle excitations. They are determined by fitting exactly calculated spectral moments. The resulting self-energy consists of a local and a non-local part. The higher correlation functions entering the spin-dependent local part can be expressed as functionals of the single-electron spectral density. Under certain conditions for the decisive model parameters (Coulomb interaction U, Bloch bandwidth W, band occupation n, temperature T) the local part of the self-energy gives rise to a spin-dependent band shift, thus allowing for spontaneous band magnetism. As a function of temperature, second-order phase transitions are found away from half-filling, but close to half-filling, the system exhibits a tendency towards first-order transitions. The non-local self-energy part is determined by use of proper two-particle spectral densities. Its main influence concerns a (possibly spin-dependent) narrowing of the quasiparticle bands with the tendency to stabilize magnetic solutions. The non-local self-energy part disappears in the limit of infinite dimensions. We present a full evaluation of the Hubbard model in terms of quasiparticle densities of states, quasiparticle dispersions, magnetic phase diagram, critical temperatures (T_c, T_N) as well as spin and particle correlation functions. Special attention is focused on the non-locality of the electronic self-energy, for which some rigorous limiting cases are worked out.     

Renormalization of relativistic self-consistent Hartree-Fock approximation

The renormalization of the relativistic self-consistent Hartree-Fock approximation is restudied. It is shown that the renormalization procedure suggested by Bielajew and Serot can be greatly simplified and the renormalization achieved in a way no more complicated than that of the relativistic self-consistent Fock approximation, if the parameters in the counterterms are allowed to be density-dependent and the renormalization of the tadpole self-energy is treated appropriately. A transformation relation between the four- and three-dimensional representation of the baryon self-energy is presented and a self-consistent Hartree-Fock scheme different from that considered by Bielajew and Serot studied. The renormalized integral equations for the baryon self-energy which includes effects from the Dirac sea are reformulated in a three-dimensional form. Explicit expressions are derived. Received: 29 August 1997 / Revised version: 30 April 1998     

On the optical conductivity of high-T c superconductors

We have solved the self-consistent equation for self-energy of a hole in a quantum antiferromagnet. The optical conductivity is estimated. The results are in good agreement with experiments and numerical simulations.     

Electroweak measurements of neutron densities in CREX and PREX at JLab,USA

We analyze microscopic many-body calculations of the nuclear symmetry energy and its density dependence. The calculations are performed in the framework of the Brueckner-Hartree-Fock and the self-consistent Green’s functions methods. Within Brueckner-Hartree-Fock, the Hellmann-Feynman theorem gives access to the kinetic energy contribution as well as the contributions of the different components of the nucleon-nucleon interaction. The tensor component gives the largest contribution to the symmetry energy. The decomposition of the symmetry energy in a kinetic part and a potential energy part provides physical insight on the correlated nature of the system, indicating that neutron matter is less correlated than symmetric nuclear matter. Within the self-consistent Green’s function approach, we compute the momentum distributions and we identify the effects of the high momentum components in the symmetry energy. The results are obtained for the realistic interaction Argonne V18 potential, supplemented by the Urbana IX three-body force in the Brueckner-Hartree-Fock calculations.     

On the local quasiparticle density of states within the asymmetric Anderson model

We calculate the local density of states for the asymmetric Anderson model by applying a self-consistent perturbation approximation for the impurity electron's self-energy. The three-resonance structure obtained in the symmetric case at low temperatures, which features a narrow central peak at the Fermi level, is found to transform into a broad single resonance with increasing asymmetry. For any asymmetry the spectral density function approaches in the high temperature limit a broad two-resonance structure.     

Solving the Kadanoff-Baym equations for inhomogeneous systems: application to atoms and molecules

We implement time propagation of the nonequilibrium Green function for atoms and molecules by solving the Kadanoff-Baym equations within a conserving self-energy approximation. We here demonstrate the usefulness of time propagation for calculating spectral functions and for describing the correlated electron dynamics in a nonperturbative electric field. We also demonstrate the use of time propagation as a method for calculating charge-neutral excitation energies, equivalent to highly advanced solutions of the Bethe-Salpeter equation.     

Some issues in a gauge model of unparticles

We address in a recent gauge model of unparticles the issues that are important for consistency of a gauge theory, i.e., unitarity and the Ward identity of the physical amplitudes. We find that non-integrable singularities arise in physical quantities like the cross section and the decay rate from the gauge interactions of unparticles. We also show that the Ward identity is violated due to the lack of a dispersion relation for charged unparticles although the Ward–Takahashi identity for general Green functions is incorporated in the model. A previous observation that the contribution of the unparticle (with scaling dimension d) to the gauge boson self-energy is a factor (2−d) of the particle’s self-energy has been extended to the Green function of triple gauge bosons. This (2−d) rule may be generally true for Green functions for any number of points of the gauge bosons. This implies that the model would be trivial even as one that mimics certain dynamical effects on gauge bosons in which unparticles serve as an interpolating field.     

Hybrid functionals and GW approximation in the FLAPW method

We present recent advances in numerical implementations of hybrid functionals and the GW approximation within the full-potential linearized augmented-plane-wave (FLAPW) method. The former is an approximation for the exchange–correlation contribution to the total energy functional in density-functional theory, and the latter is an approximation for the electronic self-energy in the framework of many-body perturbation theory. All implementations employ the mixed product basis, which has evolved into a versatile basis for the products of wave functions, describing the incoming and outgoing states of an electron that is scattered by interacting with another electron. It can thus be used for representing the nonlocal potential in hybrid functionals as well as the screened interaction and related quantities in GW calculations. In particular, the six-dimensional space integrals of the Hamiltonian exchange matrix elements (and exchange self-energy) decompose into sums over vector–matrix–vector products, which can be evaluated easily. The correlation part of the GW self-energy, which contains a time or frequency dependence, is calculated on the imaginary frequency axis with a subsequent analytic continuation to the real axis or, alternatively, by a direct frequency convolution of the Green function G and the dynamically screened Coulomb interaction W along a contour integration path that avoids the poles of the Green function. Hybrid-functional and GW calculations are notoriously computationally expensive. We present a number of tricks that reduce the computational cost considerably, including the use of spatial and time-reversal symmetries, modifications of the mixed product basis with the aim to optimize it for the correlation self-energy and another modification that makes the Coulomb matrix sparse, analytic expansions of the interaction potentials around the point of divergence at k = 0, and a nested density and density-matrix convergence scheme for hybrid-functional calculations. We show CPU timings for prototype semiconductors and illustrative results for GdN and ZnO.     

Self-consistent approximations for itinerant ferromagnets above the phase transition point

The “conserving and self-consistent” approximation scheme of Kadanoff and Baym is generalized to systems of particles of non-zero spin. The additional conservation law of the total spin of the system restricts the possible approximations for the self-energy part, and thus the approximations for the irreducible vertex part occuring in the equation for the correlation function. This guarantees, for instance, the correct behavior of the dynamical susceptibility in the long wave length limit. Two examples are discussed under these aspects: the Hartree-Fock and theT-matrix approximation for the self-energy part and the resulting susceptibility.     

Electrostatic self-force in the field of an (<Emphasis Type="Italic">n</Emphasis> + 1)-dimensional black hole: Dimensional regularization

The self-energy of a classical charged particle localized at a relatively large distance outside the event horizon of an (n + 1)-dimensional Schwarzschild–Tangherlini black hole for an arbitrary n ≥ 3 is calculated. An expression for the electrostatic Green function is derived in the first two orders of the perturbation theory. Dimensional regularization is proposed to be used to regularize the corresponding formally divergent expression for the self-energy. The derived expression for the renormalized self-energy is compared with the results of other authors.     

Remnant Fermi surface in a pseudogap regime of the two-dimensional Hubbard model at finite temperature

A precursor effect on the Fermi surface in the two-dimensional Hubbard model at finite temperatures near the antiferromagnetic instability is studied using three different itinerant approaches: the second order perturbation theory, the paramagnon theory (PT), and the two-particle self-consistent (TPSC) approach. In general, at finite temperature, the Fermi surface of the interacting electron systems is not sharply defined due to the broadening effects of the self-energy. In order to take account of those effects we consider the single-particle spectral function A(, 0) at the Fermi level, to describe the counterpart of the Fermi surface at T = 0. We find that the Fermi surface is destroyed close to the pseudogap regime due to the spin-fluctuation effects in both PT and TPSC approaches. Moreover, the top of the effective valence band is located around = (π/2,π/2) in agreement with earlier investigations on the single-hole motion in the antiferromagnetic background. A crossover behavior from the Fermi-liquid regime to the pseudogap regime is observed in the electron concentration dependence of the spectral function and the self-energy. Received 8 September 2000 and Received in final form 20 December 2000