Random Phase Approximation Results Research Articles

Efficient random phase approximation for diradicals.

We apply the analytically solvable model of two electrons in two orbitals to diradical molecules, characterized by two unpaired electrons. The effect of doubly occupied and empty orbitals is taken into account by means of random phase approximation (RPA). We show that in the static limit, the direct RPA leads to the renormalization of the parameters of the two-orbital model. We test our model by comparing its predictions for singlet-triplet splitting with the results of several multi-reference methods for a set of thirteen molecules. We find that for this set, the static RPA results are close to those of the NEVPT2 method with two orbitals and two electrons in the active space.

Dynamic polarization, quantum spectral function and effective mass for black phosphorous: Random phase approximation approach at finite temperature

In this work, the finite-temperature dynamic polarization function of black phosphorus is obtained using the random phase approximation (RPA) for the lower band of the corresponding effective Hamiltonian. The maximum temperature-dependent polarization of the orthorhombic honeycomb structure of black phosphorus is observed at ω=0.54eV for wavectors at the Fermi level. Several peaks are thus observed indicating that an overall Fermi-liquid behavior is present but with different kinds of quasiparticles. These quasiparticles appear due to the highly anisotropic energy dispersion. Experiments conducted on black phosphorous at a temperature of 10 K have a tremendous effect on the scattering mechanism. Subsequently, the quasiparticle behavior is studied through the spectral function and the effective mass, each resolved on the three components of the wave number. The resulting effective mass anisotropy causes the plasmon to disperse completely, leading to a lower resonant frequency when there is a larger mass along one of the axes. At large wavelengths, the RPA result is almost identical to that obtained from the classical plasmon dispersion.

Drag resistivity in bilayer-graphene/GaAs coupled layer system with the effect of local field corrections

Drag resistivity mediated by Coulomb interaction is a transport phenomenon in a specially separated bilayer systems. The drag resistivity is numerically analysed for both the n- and p-type charge carriers between the bilayer-graphene and a GaAs layer, with an insulating barrier by using random phase approximation (RPA). The RPA method does not include exchange and correlation effects, which are included by assuming the local field correction (LFC) in effective interactions. Because of the LFC effects, the drag resistivity is found enhanced compared to the measured results of RPA. The present bilayer system shows a comparison between effect of electron–electron (e–e) repulsive and electron–hole (e–h) attractive interactions in Boltzmann regime for low temperature limit. Different masses of electrons and holes in GaAs layer are analysed, and drag resistivity is increased on increasing the effective mass of the charge carriers. The dependency of drag resistivity on temperature, concentration, interlayer separation, width of the drag layer and dielectric constant of barrier shows a consistent behaviour.

Random-Phase Approximation in Many-Body Noncovalent Systems: Methane in a Dodecahedral Water Cage.

The many-body expansion (MBE) of energies of molecular clusters or solids offers a way to detect and analyze errors of theoretical methods that could go unnoticed if only the total energy of the system was considered. In this regard, the interaction between the methane molecule and its enclosing dodecahedral water cage, CH4···(H2O)20, is a stringent test for approximate methods, including density functional theory (DFT) approximations. Hybrid and semilocal DFT approximations behave erratically for this system, with three- and four-body nonadditive terms having neither the correct sign nor magnitude. Here, we analyze to what extent these qualitative errors in different MBE contributions are conveyed to post-Kohn-Sham random-phase approximation (RPA), which uses approximate Kohn-Sham orbitals as its input. The results reveal a correlation between the quality of the DFT input states and the RPA results. Moreover, the renormalized singles energy (RSE) corrections play a crucial role in all orders of the many-body expansion. For dimers, RSE corrects the RPA underbinding for every tested Kohn-Sham model: generalized-gradient approximation (GGA), meta-GGA, (meta-)GGA hybrids, as well as the optimized effective potential at the correlated level. Remarkably, the inclusion of singles in RPA can also correct the wrong signs of three- and four-body nonadditive energies as well as mitigate the excessive higher-order contributions to the many-body expansion. The RPA errors are dominated by the contributions of compact clusters. As a workable method for large systems, we propose to replace those compact contributions with CCSD(T) energies and to sum up the remaining many-body contributions up to infinity with supermolecular or periodic RPA. As a demonstration of this approach, we show that for RPA(PBE0)+RSE it suffices to apply CCSD(T) to dimers and 30 compact, hydrogen-bonded trimers to get the methane-water cage interaction energy to within 1.6% of the reference value.

Coulomb drag study in graphene/GaAs bilayer system with the effect of local field correction and dielectric medium

The drag resistivity is measured numerically for electron-electron (e-e) and electron-hole (e-h) coupled layer system composed of single layer graphene and two-dimensional (2D) GaAs layer separated by a barrier. The system is studied within the model of random phase approximation (RPA) and taking into account the static local field correction (LFC) and layer thickness effects in the Ballistic/Boltzmann regime. We have shown analytical expressions of non-linear susceptibility function and effective interlayer Coulomb interaction for non homogeneous dielectric environment at low temperature, high density and large interlayer separation limit. Exchange and correlation effects enhanced the drag resistivity by considering the static local field correction. Width of the layer and interlayer distance dependent local form factors (LFF) are obtained from the solution of the Poisson equation for a multi-layer dielectric medium. The effects of LFC and LFF are the function of bare inter- and intra-layer potential, which enhances the drag resistivity compare to simply measured RPA results. Enhanced drag resistivity also measured for e-h bilayer system where the hole layer is considered for 2D GaAs (drag layer), cause of larger effective mass of hole compare to the electron. Similarly, e-e and e-h bilayer system measured the enhanced drag resistivity due to LFC effects.

Quenching factor of Gamow-Teller and spin dipole giant resonances

Gamow-Teller (GT) and spin-dipole (SD) strength distributions of four doubly magic nuclei $^{48}$Ca, $^{90}$Zr, $^{132}$Sn and $^{208}$Pb are studied by the self-consistent Hartree-Fock plus random phase approximation (RPA) method. The Skyrme forces SAMi and SAMi-T without/with tensor interactions are adopted in our calculations. The calculated strengths are compared with available experimental data. The RPA results of GT and SD strengths of all four nuclei show fine agreement with observed GT and SD resonances in energy. A small GT peak below the main GT resonance is better described by the Skyrme interaction SAMi-T with the tensor terms. The quenching factors for GT and SD are extracted from the comparisons between RPA results and experimental strengths. It is pointed out that the quenching effect on experimental SD peaks is somewhat modest compared with that on GT peaks in the four nuclei.

Systematic study of giant quadrupole resonances with the subtracted second random-phase approximation: Beyond-mean-field centroids and fragmentation

A systematic analysis of giant quadrupole resonances is performed for several nuclei, from $^{30}\mathrm{Si}$ to $^{208}\mathrm{Pb}$, within the subtracted second random-phase-approximation (SSRPA) model in the framework of the energy-density-functional theory. Centroid energies and widths of the isoscalar giant quadrupole resonances are compared with the corresponding random-phase-approximation (RPA) values. We find lower SSRPA centroid energies compared to the RPA values leading, in general, to a better agreement with the experimental data. As far as the widths are concerned, we observe for both SSRPA and RPA cases a global attenuation of the single-particle Landau damping going from lighter to heavier nuclei, and we obtain, systematically, larger widths in the SSRPA model compared to the RPA case. For some selected nuclei for which high-resolution ($p,{p}^{\ensuremath{'}}$) experimental data are available, namely $^{40}\mathrm{Ca}$, $^{90}\mathrm{Zr}$, $^{120}\mathrm{Sn}$, and $^{208}\mathrm{Pb}$, the theoretical strength distributions are directly compared with the experimental spectra. We observe a significant improvement, with respect to RPA results, in the description of the spreading widths and of the fragmentation of the obtained spectra, due to the coupling between one-particle--one-hole and two-particle--two-hole configurations.

Energy loss of α-particle moving in warm dense deuterium plasma: Role of local field corrections

We theoretically study the energy loss of α-particles traveling in the warm dense plasma (WDP) of deuterium (D) with temperatures from 10 to 100 eV and electron number densities from 1023 to 1024 cm−3. Beyond the random phase approximation (RPA) model, the extended Mermin dielectric function (MDF) model including the static and dynamic local field corrections (LFC) is employed in the calculations. Compared with the static LFC, the dynamic LFC introduced in the extended MDF model gives rise to a more significant departure from the RPA result. For the plasma conditions focused in this work, the departure induced by dynamic LFC reaches almost ∼30%, which may be detected in the inertial confinement fusion (ICF) related experiment. Moreover, we find that the effect of static e-e collision may be of importance (unimportance) for the WDP of D with a temperature of tens (hundreds) of eV. Our findings may be important for ICF ignition since the uncertainty induced by the correlation effects between plasma component particles is crucial for the prediction of α-particle heating in fusion plasmas.

Significance of distinct electron-correlation effects in determining the ( P,T )-odd electric dipole moment of Yb171

Parity and time-reversal violating electric dipole moment (EDM) of $^{171}$Yb is calculated accounting for the electron correlation effects over the Dirac-Hartree-Fock (DHF) method in the relativistic Rayleigh-Schr\"odinger many-body perturbation theory, with the second (MBPT(2) method) and third order (MBPT(3) method) approximations, and two variants of all-order relativistic many-body approaches, in the random phase approximation (RPA) and coupled-cluster (CC) method with singles and doubles (CCSD method) framework. We consider electron-nucleus tensor-pseudotensor (T-PT) and nuclear Schiff moment (NSM) interactions as the predominant sources that induce EDM in a diamagnetic atomic system. Our results from the CCSD method to EDM ($d_a$) of $^{171}$Yb due to the T-PT and NSM interactions are found to be $d_a = 4.85(6) \times 10^{-20} \langle \sigma \rangle C_T \ |e| \ cm$ and $d_a=2.89(4) \times 10^{-17} {S/(|e|\ fm^3)}$, respectively, where $C_T$ is the T-PT coupling constant and $S$ is the NSM. These values differ significantly from the earlier calculations. The reason for the same has been attributed to large correlation effects arising through non-RPA type of interactions among the electrons in this atom that are observed by analyzing the differences in the RPA and CCSD results. This has been further scrutinized from the MBPT(2) and MBPT(3) results and their roles have been demonstrated explicitly.

Relation of E1 pygmy and toroidal resonances

A possible relation of low-lying E1 strength ("pygmy resonance") and toroidal strength is analyzed by using Skyrme random-phase-approximation (RPA) results for the strength functions, transition densities and current fields in 208Pb. It is shown that the irrotational pygmy motion can appear as a local manifestation of the collective vortical toroidal dipole resonance (TDR) at the nuclear surface. The RPA results are compared to unperturbed (1ph) ones.

Low excitations of 16O using generalized density matrix random phase approximation GDRPA

The random phase approximation (RPA) equations based on the generalized density matrix (GDM), the so-called GDRPA are reformulated in a more compact matrix form, which renders the method especially suitable for realistic nuclear structure calculations. The GDRPA Hamiltonian is expressed in terms of the one-body particle–particle (pp) and hole–hole (hh) density matrices, and the nuclear force contributes not only in the particle–hole (ph) channel, as in normal ph-RPA, but also in the pp and hh channels. The Hamiltonian is diagonalized iteratively starting from initial guess values and the iterating process is carried out until self-consistency is achieved. The calculation in the model space 1p, 1d and 2s using Warburton and Brown interaction WBP is performed for 16 O . The GDRPA in the ph shell model calculations is tested, by comparing the energy eigenvalues and the electron scattering form factors with the results of the normal RPA and with the available experimental data.

Linear response within the projector-based renormalization method: many-body corrections beyond the random phase approximation

The explicit evaluation of linear response coefficients for interacting many-particle systems still poses a considerable challenge to theoreticians. In this work we use a novel many-particle renormalization technique, the so-called projector-based renormalization method, to show how such coefficients can systematically be evaluated. To demonstrate the prospects and power of our approach we consider the dynamical wave-vector dependent spin susceptibility of the two-dimensional Hubbard model and also determine the subsequent magnetic phase diagram close to half-filling. We show that the superior treatment of (Coulomb) correlation and fluctuation effects within the projector-based renormalization method significantly improves the standard random phase approximation results.

Local Correlation Effects on the s±- and s++-Wave Superconductivities Mediated by Magnetic and Orbital Fluctuations in the Five-Orbital Hubbard Model for Iron Pnictides

We investigate the electronic state and the superconductivity in the five-orbital Hubbard model for iron pnictides by using the dynamical mean-field theory in conjunction with the Eliashberg equation. The renormalization factor exhibits significant orbital dependence resulting in the large change in the band dispersion as observed in recent ARPES experiments. The critical interactions towards the magnetic, orbital and superconducting instabilities are suppressed as compared with those from the random phase approximation (RPA) due to local correlation effects. Remarkably, the \(s_{++}\)-pairing phase due to the orbital fluctuation is largely expanded relative to the RPA result, while the \(s_{\pm}\)-pairing phase due to the magnetic fluctuation is reduced.

Magnetic Susceptibility of Quasi-two-dimensional Cuprate Antiferromagnets

Abstract Parallel magnetic susceptibility temperature dependence of the high-TC superconducting parent compound La2CuO4 is calculated in both antiferromagnetic (AFM) and paramagnetic phase. By making use of the quantum Heisenberg three-dimensional AFM model including the in-plane spin anisotropy, the calculation is performed within the framework of three different theories: Green’s function theory in random-phase approximation (RPA), linear spinwave (LSW) theory and mean-field (MF) theory. The results suggest that at low temperatures quantum spin fluctuations play an important role, while at the temperatures above the critical one short-range correlations have a great impact on the behavior of the system. This leads to the discrepancy between RPA and MF results, since the later neglects the above phenomena. Further, LSW theory expectedly agrees with RPA results only at low temperatures where the magnon interactions are negligible. Comparison to the theoretical and experimental results quoted in literature confirms that RPA method presents the most appropriate method among the applied ones, suggesting that this approach is satisfactory in the case of the parallel magnetic susceptibility, while in order to reproduce the transversal one, spin-orbit coupling must be included.

Dynamical response function in sodium and aluminum from time-dependent density-functional theory

We present a detailed study of the dynamical electronic response in bulk sodium and aluminum within time-dependent density-functional theory (TDDFT). The poor results of the random-phase approximation (RPA) and the time-dependent local-density approximation (TDLDA) in sodium are greatly improved by the approximate inclusion of the finite lifetimes of electrons and holes via a modified independent-particle polarizability, which brings the calculated spectra into good agreement with experiment. For aluminum the changes are less visible, but at some values of momentum-transfer lifetime effects are necessary to obtain qualitatively correct spectra. The double-peak structure in aluminum, induced by band-structure effects, is partially washed out by the inclusion of the finite lifetimes. The latter do not, however, create a double peak by themselves as they do in the case of the homogeneous electron gas. Studying the performance of different time-dependent and nonlocal TDDFT kernels, we conclude that the Gross-Kohn, Corradini et al., and the Hubbard local-field factors improve the spectra compared to the RPA results. However, the results agree less well with experiment than those obtained using TDLDA with added lifetime effects. These results apply to both the loss spectra and the plasmon dispersion.

Applying full conserving dielectric function to the energy loss straggling

AbstractThe purpose of this paper is to calculate proton energy loss straggling using a full conserving dielectric function (FCDF) for plasmas at any degeneracy. This dielectric function takes into account plasma electron-electron collision considering density, momentum, and energy conservation. When only momentum conservation law is accomplished, the FCDF reproduces the well known Mermin dielectric function, when none of the conservations laws are obeyed, the random phase approximation (RPA) is recovered. Then, the FCDF is applied for the first time to the determination of the energy loss straggling. Differences among diverse dielectric functions to determine straggling follow the same behavior for all kind of plasmas then, they do not depend on the plasma degeneracy but essentially do on the value of the collision frequency. These discrepancies can rise up to 5% between FCDF values and the Mermin ones, and 2% between the FCDF ones and RPA ones for plasma with high enough collision frequency. The similarity between FCDF and RPA results is not surprising, as all conservation laws are also considered in RPA dielectric function. The fact that FCDF and RPA give similar results and the fact that FCDF considers electron-electron collisions and RPA does not, means that latter collisions are not significant for energy loss straggling calculations.

Second RPA with Skyrme Interaction

The Second Random Phase Approximation (RPA) is a natural extension of RPA obtained by introducing more general excitation operators where two particle-two hole configurations, in addition to the one particle-one hole ones, are considered. Some Second RPA results with Skyrme force in 16O are presented. Different levels of approximation are compared and in particular the quality of the diagonal approximation is tested. The issue of the rearrangement terms to be used in the matrix elements beyond the standard RPA ones, when density-dependent force are used, is briefly discussed. Two approximated, and generally used, schemes are used: the rearrangement terms are neglected in the matrix elements beyond RPA or evaluated with the RPA prescription. As a general feature of Second RPA results, a several-MeV shift of the strength distribution to lower energies is systematically found with respect to RPA distributions.

Proton stopping using a full conserving dielectric function in plasmas at any degeneracy

In this work, we present a dielectric function including the three conservation laws (density, momentum and energy) when we take into account electron-electron collisions in a plasma at any degeneracy. This full conserving dielectric function (FCDF) reproduces the random phase approximation (RPA) and Mermin ones, which confirms this outcome. The FCDF is applied to the determination of the proton stopping power. Differences among diverse dielectric functions in the proton stopping calculation are minimal if the plasma electron collision frequency is not high enough. These discrepancies can rise up to 2% between RPA values and the FCDF ones, and to 8% between the Mermin ones and FCDF ones. The similarity between RPA and FCDF results is not surprising, as all conservation laws are also considered in RPA dielectric function. Even for plasmas with low collision frequencies, those discrepancies follow the same behavior as for plasmas with higher frequencies. Then, discrepancies do not depend on the plasma degeneracy but essentially do on the value of the plasma collision frequency.

Single-Impurity Problem in Iron-Pnictide Superconductors

Single impurity problem in iron-pnictide superconductors is investigated by solving Bogoliubov-de Gennes (BdG) equation in the five-orbital model, which enables us to distinguish s$_{+-}$ and s$_{++}$ superconducting states. We construct a five-orbital model suitable to BdG analysis. This model reproduces the results of random phase approximation in the uniform case. Using this model, we study the local density of states around a non-magnetic impurity and discuss the bound-state peak structure, which can be used for distinguishing s$_{+-}$ and s$_{++}$ states. A bound state with nearly zero-energy is found for the impurity potential $I\sim 1.0$ eV, while the bound state peaks stick to the gap edge in the unitary limit. Novel multiple peak structure originated from the multi-orbital nature of the iron pnictides is also found.

Controlled expansion for certain non-Fermi-liquid metals

The destruction of Fermi liquid behavior when a gapless Fermi surface is coupled to a fluctuating gapless boson field is studied theoretically. This problem arises in a number of different contexts in quantum many body physics. Examples include fermions coupled to a fluctuating transverse gauge field pertinent to quantum spin liquid Mott insulators, and quantum critical metals near a Pomeranchuk transition. We develop a new controlled theoretical approach to determining the low energy physics. Our approach relies on combining an expansion in the inverse number (N) of fermion species with a further expansion in the parameter \epsilon = z_b -2 where z_b is the dynamical critical exponent of the boson field. We show how this limit allows a systematic calculation of the universal low energy physics of these problems. The method is illustrated by studying spinon fermi surface spin liquids, and a quantum critical metal at a second order electronic nematic phase transition. We calculate the low energy single particle spectra, and various interesting two particle correlation functions. In some cases deviations from the popular Random Phase Approximation results are found. Some of the same universal singularities are also calculated to leading non-vanishing order using a perturbative renormalization group calculation at small N extending previous results of Nayak and Wilczek. Implications for quantum spin liquids, and for Pomeranchuk transitions are discussed. For quantum critical metals at a nematic transition we show that the tunneling density of states has a power law suppression at low energies.