Fast impurity solver for dynamical mean field theory based on second order perturbation around the atomic limit

This paper proposes an impurity solver for the dynamical mean field theory (DMFT) study of the Mott insulators, which is based on the second order perturbation of the hybridization function. After careful benchmarking with quantum Monte Carlo results on the anti-ferromagnetic phase of the Hubbard model, it concludes that this impurity solver can capture the main physical features in the strong coupling regime and can be a very useful tool for the LDA (local density approximation) +,DMFT studies of the Mott insulators with long range order.     

Many-body perturbation theory using the density-functional concept: beyond the GW approximation

We propose an alternative formulation of many-body perturbation theory that uses the density-functional concept. Instead of the usual four-point integral equation for the polarizability, we obtain a two-point one, which leads to excellent optical absorption and energy-loss spectra. The corresponding three-point vertex function and self-energy are then simply calculated via an integration, for any level of approximation. Moreover, we show the direct impact of this formulation on the time-dependent density-functional theory. Numerical results for the band gap of bulk silicon and solid argon illustrate corrections beyond the GW approximation for the self-energy.     

Excited states from range-separated density-functional perturbation theory

We explore the possibility of calculating electronic excited states by using perturbation theory along a range-separated adiabatic connection. Starting from the energies of a partially interacting Hamiltonian, a first-order correction is defined with two variants of perturbation theory: a straightforward perturbation theory and an extension of the Görling–Levy one that has the advantage of keeping the ground-state density constant at each order in the perturbation. Only the first, simpler, variant is tested here on the helium and beryllium atoms and on the hydrogen molecule. The first-order correction within this perturbation theory improves significantly the total ground- and excited-state energies of the different systems. However, the excitation energies mostly deteriorate with respect to the zeroth-order ones, which may be explained by the fact that the ionisation energy is no longer correct for all interaction strengths. The second (Görling–Levy) variant of the perturbation theory should improve these results but has not been tested yet along the range-separated adiabatic connection.     

BSSE-free second order intermolecular perturbation theory II. Sample calculations on hydrogen-bonded complexes

The second order BSSE-free intermolecular perturbation theory based on the ‘Chemical Hamiltonian Approach’ (CHA), which was developed in the first part of this paper is applied to several hydrogen bonded systems using a variety of different basis sets. The results show that the second order BSSE-free interaction energy is remarkably close to that obtained by the conventional MP2 interaction energy if the latter is properly CP corrected. This shows that these two independent and conceptually different approaches–the classical Boys-Bernardi scheme and the CHA method–strongly corroborate each other.     

Investigation of the spin generation using the perturbation theory in the long wavelength limit

An investigation of the electronic spin-generation in gallium arsenide is performed using the perturbation theory of the spin transport model in the long wavelength limit, where electron–electron and electron–phonon interactions are ignored. The spin polarizations of the conduction-band-electrons in dependences of the excited one- and two-photon energies are estimated. For both cases, the spin-polarization is found to depolarize for excitation energies equal to or larger than the energy gap of the split-off band to the conduction band. The results, however, show that an enhancement of the spin-polarization is achieved by multiphoton excitation of the bulk semiconductors. The calculated results are compared with those obtained in recent experiments. A good agreement between theory and experiment is obtained.     

Electrical resistivity in the strong-correlation limit of the emery model

On the basis of the Emery model in the limitU _d , the electrical resistivity is calculated by means of the memory function method. The inelastic scattering of oxygen holes on transverse and longitudinal antiferromagnetic spin fluctuations of copper spins is considered. Assuming a Fermi-liquid model for the dynamic spin susceptibility, the two-dimensional spin-fluctuation resistivity reveals a crossover from a quadratic to a linear temperature dependence. This may explain the normal-state basal-plane resistivity of high-T _c superconductors, in particular the observed non-linear temperature dependences.     

Application of density-functional perturbation theory to calculate nonlinear polarizabilities of helium-like systems

Density-based perturbation theory within the Hohenberg-Kohn (HK) formalism of density functional theory (DFT), developed recently by us, is employed to calculate hyperpolarizabilities of helium-like ions from their ground-state densities obtained from their respective Hylleraas wavefunctions. The only approximation made is that of the local density (LDA) for exchange and correlation. Use of densities — instead of wavefunctions — in density-based perturbation theory together with simple approximate energy functionals makes our calculations much simpler than those based on wavefunctions. They lead, however, to accurate results.     

Thermodynamic limit in the elastic triangle: perturbation theory

The equilibrium state of a triangular pile of particles, interconnected by linear springs and subjected to the force of gravity, is explored algebraically. A subset of the springs is treated as weak in relation to the others and perturbation theory is used to obtain the zero order and first order expressions for the equilibrium positions of the particles. The zero order results prove to satisfy a thermodynamic limit. In contrast, the first order results fail to exhibit a thermodynamic limit because the perturbation expansion parameter proves to be a function of the number of rows of particles in the triangle.     

Higher order perturbation theory of exponential Lagrangians: Fourth order

We define the vacuum expectation value of the time-ordered product of four exponentials of free massless scalar fields as a continuous linear functional over a suitable test function space using minimal singularity as a criterion.Work supported in part by Banco National do Desenvolvimento Econômico, Brazil.     

A simplified structure for the second order cosmological perturbation equations

Increasingly accurate observations of the cosmic microwave background and the large scale distribution of galaxies necessitate the study of nonlinear perturbations of Friedmann–Lemaitre cosmologies, whose equations are notoriously complicated. In this paper we present a new derivation of the governing equations for second order perturbations within the framework of the metric-based approach that is minimal, as regards amount of calculation and length of expressions, and flexible, as regards choice of gauge and stress–energy tensor. Because of their generality and the simplicity of their structure our equations provide a convenient starting point for determining the behaviour of nonlinear perturbations of FL cosmologies with any given stress–energy content, using either the Poisson gauge or the uniform curvature gauge.     

A general approach to specific second order ordinary differential equations using homotopy perturbation method

Homotopy perturbation method is used to solve specific second order ordinary differential equations and tested for different examples. The results obtained demonstrate efficiency of the proposed method.     

Central limit theorem for the Lorentz process via perturbation theory

The Markov partition of the Sinai billiard allows the following heuristic interpretation for the Lorentz process with a ²-periodic configuration of scatterers: while executing a (non-Markovian) random walk on ², and particle changes its internal state according to the symbolic dynamics defined by the Markov partition. This picture can be formalized and then the Lorentz process appears as the limit of a sequence of (Markovian!) random walks with a finite but increasing number of internal states and the central limit theorem can be proved for it by perturbational expansions with uniformly bounded — in a sence related to the Perron-Frobenius theorem — coefficients and uniform remainder terms.     

Towards a description of the Kondo effect using time-dependent density-functional theory

We demonstrate that the zero-temperature conductance of the Anderson model can be calculated within the Landauer formalism combined with static density-functional theory. The proposed approximate functional is based on finite-temperature density-functional theory and yields the exact Kohn-Sham potential at the particle-hole symmetric point. Furthermore, in the limit of zero temperature it correctly exhibits a derivative discontinuity which is shown to be essential to reproduce the conductance plateau. On the other hand, at the Kondo temperature the exact Kohn-Sham conductance overestimates the real one by an order of magnitude. To understand the failure of density-functional theory, we resort to its time-dependent version and conclude that the suppression of the Kondo resonance must be attributed to dynamical exchange-correlation corrections.     

Calculation of the interruption function in the fourth order of the perturbation theory

General expressions for fourth-order terms for calculating the interruption function S(b) in terms of the perturbation theory are derived for molecules with different symmetry properties and arbitrary trajectories of the relative motion of colliding molecules. An expression for a quadruple integral over time appearing in the definition of new resonance functions is written in terms of the Fourier transform of the coefficients of the intermolecular interaction potential.