Self-consistent Perturbation Theory Research Articles

SELF-CONSISTENT PERTURBATION EXPANSIONS FOR SINGLE-IMPURITY-EXCHANGE-MODELS

Combining self-consistent perturbation theory with conventional renormalization group equations, a new systematic approach to Kondo-type models is developed, which yields analytical expressions for universal quantities like pseudofermion exponents and large effective couplings, usually out of reach from perturbative calculations. The new approach is related to the parquet-treatment of the x-ray-edge-singularity by Noziéres and coworkers in the late sixties and makes no use of a linearization of the band-electron-dispersion-relation, which is crucial for the Bethe Ansatz, conformal field theory, or numerical renormalization group treatment of the models. In addition it covers 1/N2-corrections to the well-known Non-Crossing-Approximation.

An integrated modal approach to waveguide reverberation

In shallow-water environments scattering from rough surfaces and volume inhomogeneities acts to degrade sonar performance. An efficient normal mode method has been developed to model the resulting reverberation. The self-consistent perturbation theory of Schmidt and Kuperman [J. Acoust. Soc. Am. 97, 2199–2210 (1995)] has been reformulated in terms of normal modes to handle scattering from rough fluid and elastic interfaces. A similar, recently developed volume scattering theory is used to model the effects of sound speed and density fluctuations in the seabed and water column. The two theories are integrated numerically and used to contrast the different scattering mechanisms. Waveguide propagation effects are seen to be extremely important. Spatial correlation and modal cross-correlation statistics are estimated and used to study decorrelation of the sound field. Excellent agreement with the wave-number integration implementation by Schmidt and Kuperman is demonstrated for the case of rough interface scattering, with the modal approach requiring significantly less computation for low-frequency shallow-water scenarios.

The ozonide anion: A theoretical study

Complete active space self-consistent field (CASSCF) and CASSCF second-order perturbation theory (CASPT2) methods have been used for the geometry optimization and calculation of harmonic and fundamental frequencies of the ozonide ion (O−3) and the ozonide lithium complex (Li+O−3). For O−3 harmonic frequencies have also been obtained using the coupled-cluster method, CCSD(T). Infrared intensities are computed from dipole moment derivatives at the CASSCF level. The predicted equilibrium geometry for O−3 is ROO=1.361 Å and ∠OOO=115.4°, and the fundamental frequencies are ν1=989 cm−1, ν2=556 cm−1, ν3=870 cm−1 [experimental values are ROO=1.36±0.02 Å, ∠OOO=111.8±2.0°, ν1=975(50) cm−1, ν2=550(50) cm−1, ν3=880(50) cm−1]. Corresponding data for the lithium ozonide complex have also been obtained. The presented data contradict the previous interpretation of the IR and Raman spectrum obtained after codeposition of ozone and alkali atoms in N2, argon, or neon matrices. The presence of the lithium cation raises the asymmetric stretch frequency to about 940 cm−1, which is contradictory to assumptions made in the assignments of the matrix spectra. Calculations made in a dielectric medium strongly suggest that the effect of the matrix on the IR spectrum is small for O−3 itself. The dissociation and atomization energies of O−3 are found to be in agreement with experiment.

Model for a strongly correlated insulator: FeSi.

Prompted by suggestions that FeSi may be a strongly correlated insulator, somewhat analogous to the Kondo insulators, we study the properties of a two-band Hubbard model Hamiltonian in the infinite-dimensional limit. By a calculation of the one-particle self-energy using self-consistent second-order perturbation theory we are able to calculate the temperature dependence of the magnetic susceptibility and of angle-resolved photoemission spectra. The results are in fair agreement with experimental data on FeSi.

Field-theoretic approximations for normal diffusion in random velocity fields.

The motion of a classical Brownian particle entrained in a fluid with random, time-independent velocity fields is discussed. Two approaches to calculating the disorder-averaged Green's function are presented, both based upon a functional-integral formulation. A renormalization group (RG) approach proves to be less satisfactory than does a self-consistent perturbation theory approach, which reproduces the well-known direct interaction approximation. An explicit comparison of the results with Monte Carlo data is made in two dimensions. The relationship between the present results and the case of diffusion in a solid, where RG provides a superior answer, is discussed in physical terms.

Loop-expansion study of the single-hole spectral function in the t-J model.

We consider a single hole in the t-J model where the Heisenberg and the hole-hopping terms are expanded in powers of the spin-deviation operators. The lowest order corresponds to the linear spin-wave approximation and leads to an effective Hamiltonian studied earlier by means of self-consistent perturbation theory. In this work we shall include all terms generating up to two-loop diagrams in the perturbative expansion of the single-hole Green's function. The hard-core constraints are partially respected and the overall effect gives a renormalization factor of 1.158 to the hopping parameter t. The vertex that describes the process where a spin wave is absorbed and emitted at the same time by the hole is far more important than others. We find that the numerical solutions of Dyson's equation including all two-loop diagrams lower considerably the single-hole ground-state energies over the previous one-loop results and our results on the 4\ifmmode\times\else\texttimes\fi{}4 lattice are in better agreement with those obtained by exact diagonalization in the physical regime (small J/t). Our method can provide numerical solutions to the hole Green's function on very large lattices. We find that with the inclusion of the two-loop diagrams the spectral function retains all its features found in the one-loop calculation and the bandwidth, the quasiparticle residues, and the ``string'' excitations feel very small corrections.

Classical diffusion in strong random media

We study classical diffusion of particles in random media. Although many of our results are general, we focus on the case of an ion in a three-dimensional medium with random, quenched charge centers obeying bulk charge neutrality. Within a functional-integral framework, we calculate the effective diffusion coefficients by first-order and second-order self-consistent perturbation theory (with a Gaussian reference in both cases). We also carry out a one-loop order momentum space renormalization group calculation. The self-consistent methods are complicated numerically and fail beyond intermediate disorder strengths. In contrast, the renormalization group calculation gives an analytical result that appears valid even to high disorder strengths. The methodology, generally applicable to a quantitative calculation of effective diffusion coefficients in disordered media, resolves deficiencies in self-consistent perturbation theory approaches to this class of problems.

Single impurity models in the strong-coupling regime

Abstract A systematic approach, which combines renormalization group equations and self-consistent perturbation theory for the dynamical properties of single impurity exchange models (which hitherto were obtained from numerical results or from approximations), analytically furnishes universal quantities like pseudofermion exponents and large effective couplings, depending on the symmetry of the underlying model.

Octet-decuplet baryon mass splittings from self-consistent one-loop perturbation theory

The bag model of confined relativistic quarks in chiral-invariant interaction with scalar, pseudoscalar, vector, and pseudovector mesons, as well as gluons, is used to calculate the masses and wave functions of the spin-1/2 baryon octet and spin-3/2 decuplet, using selfconsistent Brillouin-Wigner bound state perturbation theory. Chiral symmetry breaking is invoked with the sigma model. SU (6) and SU (3) symmetries are broken by the experimental meson spectrum, and a strange quark mass. Mass corrections are calculated to one loop order, limited to the baryons of the octet and decuplet and the lowest lying mesons. Encouraging results are obtained, especially for theΔ — N and theΣ — Λ splittings. Convergence and stability have not been demonstrated, but are evidently improved by the self-consistency requirement. An initial parameter tuning gives a fit to all the octet and decuplet masses within ≦0.02 GeV, at the price of choosing the bag radius, the non-strange baryon input bag mass, and the strange quark mass. Even these small discrepancies can be dramatically reduced by fine-tuning the vector meson coupling and including an instanton contribution peculiar to theΛ.

NMR relaxation rate in the Hubbard model in high dimensions.

The NMR relaxation rate in the Hubbard model in high dimensions is investigated. First, by an analysis of the response functions, it is shown that, in the infinite-dimensional models, the intersite correlation does not directly affect the local response of the system. A simple approximation to consider the effects of the finite dimensions is then presented, and effects of the antiferromagnetic (AF) correlation on the NMR relaxation rate in the finite-dimensional Hubbard model is studied by treating the interaction by the self-consistent second-order perturbation theory. It is found that at low temperatures the AF correlation seriously affects the temperature dependence of the NMR relaxation rate in contrast to the case in the infinite dimensions.

Stereoselectivity and regioselectivity in Diels–Alder reactions studied by intermolecular perturbation theory

Diels–Alder reactions of ethene, acrolein and acrylonitrile with butadiene and its 1-methyl, 2-methyl and 2-cyano derivatives have been studied by self-consistent field intermolecular perturbation theory. The procedure is successful in reproducing the stereochemical predictions of other theoretical techniques, and provides a way to analyse the contributions to the interaction energy and to gain theoretical insight into the effects responsible for stereoselectivity. It is less successful, however, in predicting regiochemical preferences for these reactions. Possible reasons for this are discussed.

Self-consistent perturbation theory for random matrix ensembles: II

For pt I. see ibid, vol.23, p.1555 (1990). A method to evaluate perturbations of arbitrary spectra by one of the classical ensembles was presented in a previous paper. Its application to non-trivial problems is cumbersome and I shall show that by combining the previous results with singular perturbation theory, more complicated problems can be tackled. A scaling argument is also presented to obtain a general result that goes beyond the linear repulsion regime that we discussed previously. This result is of considerable interest as it allows us to obtain a good idea of the correlation function if we, in addition, know its long-range behaviour, which can be obtained by straightforward perturbation theory.

Dynamical properties of theD=∞ Hubbard model

Dynamical response functions of the Hubbard model on an infinite dimensional lattice ([ital D]=[infinity]) are investigated by the self-consistent second-order perturbation theory with respect to the Coulomb interaction [ital U]. The vertex corrections are properly considered so that the conservation laws are satisfied, i.e., the [ital f]-sum rule is satisfied. The explicit expression for the [ital f]-sum rule is obtained in the case of infinite dimensions. It is found that even in the second-order perturbation theory the electronic states show many-body features at finite temperature and/or frequency regions: the system crosses over from the Fermi-liquid state at the low temperature and low-frequency region to the incoherent regime at high temperatures.

Accurate dipole polarizability for Cl2(X1Σ+g)

Finite-field self-consistent field and fourth-order many-body perturbation theory with single, double and quadruple substitutions from the reference wavefunction calculations are reported for the static dipole polarizability (ααβ) of chlorine CL2(X1Σ+ g). The R/a0 dependence of the mean dipole polarizability (α) and the anisotropy (Δα) around the experimental equilibrium bond length of R e = 3.756776a0 is very well approximated by , . The present estimates of αzz, αxx, α and Δα at the ground vibrational state are 42·29, 25·32, 30·98 and 16·97e2a2 0E-1 h, respectively and should be the most accurate theoretical values currently available.

Ice canopy roughness inversion and Arctic propagation loss estimates via elastic perturbation theory

Low-frequency (f≪100 Hz) boundary interaction loss in the central Arctic has been observed to exceed the losses that may be predicted by free surface Kirchhoff or MSP scattering theories, 2-D boss scattering models, or large elastic feature scattering arguments. In addition, the measured frequency dependence of the scattering loss in the Arctic (∝f1.5) is lower than that which is predicted with either the boss or the large elastic feature scattering models. Here a self-consistent elastic perturbation theory is used to estimate coherent boundary interaction loss for the Arctic scenario. Using this theory it is found that the elasticity of the ice canopy can account for a substantial decrease in the local coherent reflection coefficient in comparison with a rough free surface interaction, while the frequency dependence of the loss remains proportional to f2. Using acoustics measurements obtained by a horizontal array under the Arctic ice, a ML inversion for the ice canopy roughness statistics is obtained using the perturbation theory, and these parameters are used to estimate the loss per interaction. This loss, when combined with a ray cycle distance taken from the relevant literature, yields an estimate of scattering propagation loss (dB/km), which closely matches the data in the low-frequency regime. When the canonical roughness parameters and cycle distances from the literature are used in the theory, the estimated loss is lower, but improvements are still obtained over the free surface results. [Work supported by ONR.]

Homogeneous isotropic turbulence in randomly stirred fluids: Self-consistent mode coupling and perturbation theory

The randomly stirred model of DeDominices and Martin [Phys. Rev. A 19, 419 (1979)] is considered in the framework of self-consistent mode coupling theories of dynamic critical phenomena. It is found that the theory is finite when the forcing yields the Kolmogorov spectrum. Perturbation theory can now be set up for universal amplitudes and results agree with the renormalization group calculations of Yakhot and Orszag [Phys. Rev. Lett. 57, 1722 (1986); J. Sci. Comput. 1, 1 (1986)].

Influence of a ferromagnetic exchange interaction on the Kondo effect in Anderson impurity systems

In the usual description of heavy fermion systems by the Anderson Hamiltonian the Coulomb interaction is taken into account explicitly only betweenf-electrons. All the other parts of the Coulomb interaction, in particular the Coulomb interaction betweenf-electrons and conduction electrons, are contained only on the average in the parameters of the Hamiltonian. In this paper the ferromagnetic exchange interaction between conduction andf-electrons is added explicitly to the single-ion Anderson Hamiltonian, and its influence on the appearance of a Kondo effect in such systems is studied. This is done with help of a self-consistent perturbation theory in the hybridization and the exchange interaction. The results, which show a strong competition between the antiferromagnetic interaction induced by the hybridization off-electrons and conduction electrons are compared with the results of an earlier mean-field calculation.

A method of self-consistent perturbation theory with respect to the energy overlap integral in the Hubbard model

A method of self-consistent perturbation theory with respect to the energy overlap integral in the Hubbard model

Dielectric properties of electron gases in a quantum well wire: inter-subband modes

A self-consistent energy-functional perturbation theory is presented for electron gases confined in a quantum well wire. An analytical expression of the dynamical dielectric function is obtained both for the intra-subband and the inter-subband modes. Different from the quasi-one-dimensional wire, the inter-subband transition in this system can be taken into consideration. Plasmon excitations of inter-subband modes are discussed.

Intersubband plasmon excitations of an electron gas in a cylindrical quantum-well wire.

A self-consistent energy-functional perturbation theory is presented for an electron gas confined in a quantum-well wire. An analytical expression of the dynamic dielectric function is obtained. It is found that besides the intrasubband mode, when the angular quantization is taken into consideration, intersubband plasmon modes exist in the single-quantum-well-wire structure. These intersubband modes have excitation energies well beyond the single-particle excitation continuum, and they are out of Landau damping. It is resonable to expect that these intersubband plasmons should be observable in experiment.