Showing papers on "Random phase approximation published in 2004"

Frequency-dependent local interactions and low-energy effective models from electronic structure calculations

Abstract: We propose a systematic procedure for constructing effective models of strongly correlated materials. The parameters, in particular the on-site screened Coulomb interaction $U$, are calculated from first principles, using the random-phase approximation. We derive an expression for the frequency-dependent $U(\ensuremath{\omega})$ and show, for the case of nickel, that its high-frequency part has significant influence on the spectral functions. We propose a scheme for taking into account the energy dependence of $U(\ensuremath{\omega})$, so that a model with an energy-independent local interaction can still be used for low-energy properties.

Quasiparticle random phase approximation based on the relativistic Hartree-Bogoliubov model. II. Nuclear spin and isospin excitations

Abstract: The proton-neutron relativistic quasiparticle random-phase approximation (PN-RQRPA) is formulated in the canonical single-nucleon basis of the relativistic Hartree-Bogoliubov model, for an effective Lagrangian characterized by density-dependent meson-nucleon couplings. The model includes both the T = 1 and T = 0 pairing channels. Pair configurations formed from the fully or partially occupied states of positive energy in the Fermi sea, and the empty negative-energy states from the Dirac sea, are included in PN-RQRPA configuration space. The model is applied to the analysis of charge-exchange modes: isobaric analog resonances and Gamow-Teller resonances.

Microscopic nature of the pygmy dipole resonance: the stable Ca isotopes.

Abstract: The electric dipole strength distribution in 44Ca has been measured up to 10 MeV in high resolution photon scattering experiments for the first time. The data obtained have been compared to earlier measurements on (40,48)Ca in order to view the evolution of the electric pygmy dipole resonance (PDR). Calculations that were performed within the framework of the microscopic extended theory of finite Fermi systems, which adds contributions of the quasiparticle-phonon coupling to random phase approximation calculations, give a qualitative agreement with the experimental data for all three isotopes. We have shown that it is necessary to include this coupling to describe the PDR.

Superconductivity in NaxCoO2 yH2O due to Charge Fluctuation

Abstract: A new mechanism of superconductivity due to charge fluctuation in the newly discovered Co-based oxide is proposed. A single-band extended Hubbard model on a triangular lattice is studied within the random phase approximation. f -wave triplet superconductivity is stabilized in the vicinity of charge–density–wave instability, which is in sharp contrast to the square-lattice case. The physical origin of the realization of the f -wave triplet state as well as its relevance to experiments are discussed.

Deformed quasiparticle random phase approximation formalism for single- and two-neutrino double β decay

Abstract: We use a deformed quasiparticle random phase approximation formalism to describe simultaneously the energy distributions of the single {beta} Gamow-Teller strength and the two-neutrino double {beta} decay matrix elements. Calculations are performed in a series of double {beta} decay partners with A=48, 76, 82, 96, 100, 116, 128, 130, 136, and 150, using deformed Woods-Saxon potentials and deformed Skyrme Hartree-Fock mean fields. The formalism includes a quasiparticle deformed basis and residual spin-isospin forces in the particle-hole and particle-particle channels. We discuss the sensitivity of the parent and daughter Gamow-Teller strength distributions in single {beta} decay, as well as the sensitivity of the double {beta} decay matrix elements to the deformed mean field and to the residual interactions. Nuclear deformation is found to be a mechanism of suppression of the two-neutrino double {beta} decay. The double {beta} decay matrix elements are found to have maximum values for about equal deformations of parent and daughter nuclei. They decrease rapidly when differences in deformations increase. We remark on the importance of a proper simultaneous description of both double {beta} decay and single Gamow-Teller strength distributions. Finally, we conclude that for further progress in the field, it would be useful to improve and completemore » the experimental information on the studied Gamow-Teller strengths and nuclear deformations.« less

Band-gap energy in the random-phase approximation to density-functional theory

Abstract: We calculate the interacting bandgap energy of a solid within the random-phase approximation (RPA) to density functional theory (DFT). The interacting bandgap energy is defined as E-g=E-RPA(N+1)+E-RPA(N-1)-2E(RPA)(N), where E-RPA(N) is the total DFT-RPA energy of the N-electron system. We compare the interacting bandgap energy with the Kohn-Sham bandgap energy, which is the difference between the conduction and valence band edges in the Kohn-Sham band structure. We show that they differ by an unrenormalized "G(0)W(0)" self-energy correction (i.e., a GW self-energy correction computed using Kohn-Sham orbitals and energies as input). This provides a well-defined and meaningful interpretation to G(0)W(0) quasiparticle bandgap calculations, but questions the physics behind the renormalization factors in the expression of the bandgap energy. We also separate the kinetic from the Coulomb contributions to the DFT-RPA bandgap energy, and discuss the related problem of the derivative discontinuity in the DFT-RPA functional. Last we discuss the applicability of our results to other functionals based on many-body perturbation theory.

Green-function theory of the Heisenberg ferromagnet in a magnetic field

Abstract: We present a second-order Green-function theory of the one- and two-dimensional $S=1∕2$ ferromagnet in a magnetic field based on a decoupling of three-spin operator products, where vertex parameters are introduced and determined by exact relations. The transverse and longitudinal spin correlation functions and thermodynamic properties (magnetization, isothermal magnetic susceptibility, specific heat) are calculated self-consistently at arbitrary temperatures and fields. In addition, exact diagonalizations on finite lattices and, in the one-dimensional case, exact calculations by the Bethe-ansatz method for the quantum transfer matrix are performed. A good agreement of the Green-function theory with the exact data, with recent quantum Monte Carlo results, and with the spin polarization of a $\ensuremath{ u}=1$ quantum Hall ferromagnet is obtained. The field dependences of the position and height of the maximum in the temperature dependence of the susceptibility are found to fit well to power laws, which are critically analyzed in relation to the recently discussed behavior in Landau's theory. As revealed by the spin correlation functions and the specific heat at low fields, our theory provides an improved description of magnetic short-range order as compared with the random phase approximation. In one dimension and at very low fields, two maxima in the temperature dependence of the specific heat are found. The Bethe-ansatz data for the field dependences of the position and height of the low-temperature maximum are described by power laws. At higher fields in one and two dimensions, the temperature of the specific heat maximum linearly increases with the field.

Charge-fluctuation-induced superconducting state in two-dimensional quarter-filled electron systems

Abstract: We investigate superconducting (SC) states in a two-dimensional extended Hubbard model at quarter-filling with on-site repulsive interaction ( U ) and nearest-neighbor repulsive interaction ( V ), which lead to spin fluctuation and charge fluctuation, respectively. The effect of charge fluctuation on the onset of the SC state is estimated by calculating pairing interaction within the random phase approximation. Solving a linearized Eliashberg equation with an anomalous self-energy as a function of both momentum and frequency, we examine the stability of a singlet SC state in a phase diagram of U and V with fixed temperatures. We obtain a novel result that the obtained SC state has d x y symmetry in the vicinity of both spin density wave (SDW) phase (\(U \gtrsim V\)) and charge density wave (CDW) phase (\(V \gtrsim U\)). The CDW-SC and SC-metal phase boundaries exhibit reentrant structures on the V – T (temperature) plane.

X-ray Thomson scattering in warm dense matter

Abstract: The scattering of photons in plasmas is an important diagnostic tool Especially, the region of warm dense matter can be probed by X-ray Thomson scattering The scattering cross-section is related to the dynamic structure factor $S(k,\omega)$ We improve the standard treatment of the scattering on free electrons within the random phase approximation (RPA) by including collisions The dielectric function is calculated in the Born-Mermin approximation The inclusion of collisions modifies the dynamic structure factor significantly in the warm dense matter regime We conclude that a theoretical description beyond the RPA is needed to derive reliable results for plasma parameters from X-ray Thomson scattering experiments

Superconductivity due to charge fluctuation in θ-type organic conductors

Abstract: Superconductivity close to charge ordering in quasi-two-dimensional 3/4-filled organic compounds is investigated for the θ-type structure. The effect of spin and charge fluctuations is calculated within random phase approximation for a relevant extended Hubbard model with both on-site ( U ) and intersite ( V ) Coulomb interactions on an anisotropic triangular lattice. It is found that both spin and charge fluctuations induce superconductivity with extended s -wave singlet pairing, which is similar to the d x y pairing state in the square lattice. In the vicinity of charge-density-wave instability, f -wave triplet pairing is also stable due to the effect of nearest-neighbor Coulomb interaction. The temperature dependences of superconductivity and charge-density-wave phase boundaries are also examined.

Effects of phonon-phonon coupling on low-lying states in neutron-rich Sn isotopes

Abstract: Starting from an effective Skyrme interaction we present a method to take into account the coupling between one- and two-phonon terms in the wave functions of excited states. The approach is a development of a finite rank separable approximation for the quasiparticle RPA calculations proposed in our previous work. The influence of the phonon-phonon coupling on energies and transition probabilities for the low-lying quadrupole and octupole states in the neutron-rich Sn isotopes is studied.

Statistics of gravity waves obtained by direct numerical simulation

Abstract: We perform direct numerical simulations of dynamic equations of decaying gravity waves on infinite-depth water. Power-law behaviour of the wave action spectrum and structure functions of the surface elevation is obtained. These power laws agree with the prediction of the weak turbulence theory. The probability density function (p.d.f.) of the surface elevation is close to the Gaussian distribution around the mean value which seems to be consistent with the random phase approximation. However, the p.d.f. deviates weakly from the Gaussian in the tail region. This deviation is significant and can be amplified by taking the Laplacian. In addition, intermittency and breakdown of the weak turbulence theory are discussed.

Metallicity and its low-temperature behavior in dilute two-dimensional carrier systems

Abstract: We theoretically consider the temperature and density dependent transport properties of semiconductor-based 2D carrier systems within the RPA-Boltzmann transport theory, taking into account realistic screened charged impurity scattering in the semiconductor. We derive a leading behavior in the transport property, which is exact in the strict 2D approximation and provides a zeroth order explanation for the strength of metallicity in various 2D carrier systems. By carefully comparing the calculated full nonlinear temperature dependence of electronic resistivity at low temperatures with the corresponding asymptotic analytic form obtained in the $T/T_F \to 0$ limit, both within the RPA screened charged impurity scattering theory, we critically discuss the applicability of the linear temperature dependent correction to the low temperature resistivity in 2D semiconductor structures. We find quite generally that for charged ionized impurity scattering screened by the electronic dielectric function (within RPA or its suitable generalizations including local field corrections), the resistivity obeys the asymptotic linear form only in the extreme low temperature limit of $T/T_F \le 0.05$. We point out the experimental implications of our findings and discuss in the context of the screening theory the relative strengths of metallicity in different 2D systems.

Two-neutron transfer in nuclei close to the drip line

Abstract: We investigate the two-neutron transfer modes induced by $(t,p)$ reactions in neutron-rich oxygen isotopes. The nuclear response to the pair transfer is calculated in the framework of continuum quasiparticle random phase approximation (cQRPA). The cQRPA allows a consistent determination of the residual interaction and an exact treatment of the continuum coupling. The $(t,p)$ cross sections are calculated within the distorted wave Born approximation approach and the form factors are evaluated by different methods: macroscopically, following the Bayman and Kallio method, and fully microscopically. A significant part of the cross section corresponds to a high-lying collective mode built entirely upon continuum quasiparticle states.

Mode-coupling model of Mott gap collapse in the cuprates: Natural phase boundary for quantum critical points

Abstract: A simple antiferromagnetic approach to the Mott transition was recently shown to provide a satisfactory explanation for the Mott gap collapse with doping observed in photoemission experiments on electron-doped cuprates. Here this approach is extended in a number of ways. RPA, mode coupling (via self-consistent renormalization), and (to a limited extent) self-consistent Born approximation calculations are compared to assess the roles of hot-spot fluctuations and interaction with spin waves. When fluctuations are included, the calculation satisfies the Mermin-Wagner theorem, and the mean-field gap and transition temperature are replaced by pseudogap and onset temperature. The model is in excellent agreement with experiments on the doping dependence of both photoemission dispersion and magnetic properties. The magnetic phase terminates in a quantum critical point (QCP), with a natural phase boundary for this QCP arising from hot-spot physics. Since the resulting T=0 antiferromagnetic transition is controlled by a generalized Stoner factor, an ansatz is made of dividing the Stoner factor up into a material-dependent part, the bare susceptibility and a correlation-dependent part, the Hubbard U, which depends only weakly on doping. From the material dependent part of the interaction, it is possible to explain the striking differences between electron- and hole-doping, despite an approximate symmetry in the doping of the QCP. The slower divergence of the magnetic correlation length in hole doped cuprates may be an indication of more Mott-like physics.

Gamow-Teller transitions and deformation in the proton-neutron random phase approximation

Abstract: We investigate reliability of Gamow-Teller transition strengths computed in the proton-neutron random phase approximation, comparing with exact results from diagonalization in full $0\ensuremath{\hbar}\ensuremath{\omega}$ shell-model spaces. By allowing the Hartree-Fock state to be deformed, we obtain good results for a wide variety of nuclides, even though we do not project onto good angular momentum. We suggest that deformation is as important or more so than pairing for Gamow-Teller transitions.

Sine-Gordon Theory for the Equation of State of Classical Hard-Core Coulomb Systems. III. Loopwise Expansion

Abstract: We present an exact field theoretical representation of an ionic solution made of charged hard spheres. The action of the field theory is obtained by performing a Hubbard–Stratonovich transform of the configurational Boltzmann factor. It is shown that the Stillinger–Lovett sum rules are satisfied if and only if all the field correlation functions are short range functions. The mean field, Gaussian and two-loops approximations of the theory are derived and discussed. The mean field approximation for the free energy constitutes an exact lower bound for the exact free energy, while the mean field pressure is an exact upper bound. The one-loop order approximation is shown to be identical with the random phase approximation of the theory of liquids. Finally, at the two-loop order and in the pecular case of the restricted primitive model, one recovers results obtained in the framework of the mode expansion theory.

Two neutrino double- β decay in deformed nuclei with an angular momentum projected basis

Abstract: Four nuclei which are proved to be 2nbb emitters ( 76 Ge, 82 Se, 150 Nd, 238 U), and four suspected, due to the corresponding Q-values, to have this property ( 148 Nd, 154 Sm, 160 Gd, 232 Th), were treated within a protonneutron quasiparticle random phase approximation spnQRPAd with a projected spherical single particle basis. The advantage of the present procedure over the ones using a deformed Woods-Saxon or Nilsson single particle basis is that the actual pnQRPA states have a definite angular momentum while all the others provide states having only K as a good quantum number. The model Hamiltonian involves a mean field term yielding the projected single particle states, a pairing interaction for alike nucleons and a dipole-dipole proton-neutron interaction in both the particle-hole sphd and particle-particle sppd channels. The effect of nuclear deformation on the single beta strength distribution as well as on the double beta Gamow-Teller transition amplitude sMGTd is analyzed. The results are compared with the existent data and with the results from a different approach, in terms of the process half-life T1/2. The case of different deformations for mother and daughter nuclei is also presented.

Collective oscillations of a confined Bose gas at finite temperature in the random-phase approximation

Abstract: We present a theory for the linear dynamics of a weakly interacting Bose gas confined inside a harmonic trap at finite temperature. The theory treats the motions of the condensate and of the noncondensate on an equal footing within a generalized random-phase approximation, which (i) extends the second-order Beliaev-Popov approach by allowing for the dynamical coupling between fluctuations in the thermal cloud, and (ii) reduces to an earlier random-phase scheme when the anomalous density fluctuations are omitted. Numerical calculations of the low-lying spectra in the case of isotropic confinement show that the present theory obeys with high accuracy the generalized Kohn theorem for the dipolar excitations and demonstrate that combined normal and anomalous density fluctuations play an important role in the monopolar excitations of the condensate. Mean-field theory is instead found to yield accurate results for the quadrupolar modes of the condensate. Although the restriction to spherical confinement prevents quantitative comparisons with measured spectra, it appears that the non-mean-field effects that we examine may be relevant to explain the features exhibited by the breathing mode as a function of temperature in the experiments carried out at JILA on a gas of $^{87}\mathrm{Rb}$ atoms.

Consequences of self-consistency violations in Hartree-Fock random phase approximation calculations of the nuclear breathing mode energy

Abstract: We provide for the first time accurate assessments of the consequences of violations of self-consistency in the Hartree-Fock based random phase approximation (RPA) as commonly used to calculate the energy E{sub c} of the nuclear breathing mode Using several Skyrme interactions we find that the self-consistency violated by ignoring the spin-orbit interaction in the RPA calculation causes a spurious enhancement of the breathing mode energy for spin unsaturated systems Contrarily, neglecting the Coulomb interaction in the RPA or performing the RPA calculations in the TJ scheme underestimates the breathing mode energy Surprisingly, our results for the {sup 90}Zr and {sup 208}Pb nuclei for several Skyrme type effective nucleon-nucleon interactions having a wide range of nuclear matter incompressibility (K{sub nm}{approx}215-275 MeV) and symmetry energy (J{approx}27-37 MeV) indicate that the net uncertainty ({delta}E{sub c}{approx}03 MeV) is comparable to the experimental one

Condensation in Hamiltonian parametric wave interaction.

Abstract: In the generic Hamiltonian problem of parametric wave interaction, we show theoretically the existence of a sudden transition leading the wave system from completely incoherent states towards highly coherent states This self-organization process is characterized by a reduction of the nonequilibrium entropy, in contrast with the H theorem of entropy growth inherent to the random phase approximation approach The mechanism underlying this intriguing condensation process is in essence a reversible nonlinear damping As a result, the lower the coherence of the initial state, the higher the coherence of the final state

Theoretical study on resonant inelastic X-ray scattering in quasi-one-dimensional cuprates

Abstract: We study theoretically the resonant inelastic x-ray scattering in quasi-one-dimensional insulating copper oxides, where the incident photon energy is tuned to the Cu 1 s –4 p absorption energy. Our attention is focused particularly on the strong momentum-transfer dependence of the spectral shape observed in recent experiments. We describe the antiferromagnetic ground state within the Hartree–Fock theory, and consider charge excitations from the ground state within the random phase approximation. By taking account of the electron correlation effects perturbatively, we obtain the detailed momentum-transfer dependence of the spectra in semiquantitative agreement with the experiments.

The Gamow-Teller resonance in finite nuclei in the relativistic random phase approximation

Abstract: Gamow-Teller (GT) resonances in finite nuclei are studied in a fully consistent relativistic random phase approximation (RPA) framework. A relativistic form of the Landau-Migdal contact interaction in the spin-isospin channel is adopted, which has a vector part as well as a time-like component. This choice ensures that the GT excitation energy in nuclear matter is correctly reproduced in the non-relativistic limit. The GT response functions of doubly magic nuclei 48Ca, 90Zr and 208Pb are calculated using the parameter set NL3 and g’ = 0.6. It is found that the effects related to Dirac sea states account for a reduction of 6-7% in the GT sum rule. The quenching of the GT strength in finite nuclei implies that the value of g’ in the relativistic model might be enlarged about 7%. The time component in the relativistic form of the Landau-Migdal force plays a little role in GT resonance energies.

Effective-mass approach to interaction effects on electronic structure in carbon nanotubes

Abstract: Effects of Coulomb interaction on the band structure are studied for carbon nanotubes in a random-phase approximation within a k · p scheme The energy gaps are strongly enhanced due to the interaction, while effects on the effective mass along the axis direction are small For realistic values of the interaction parameter, the conventional screened Hartree–Fock approximation works quite well