Random Phase Approximation Method Research Articles

G-wave pairing in BiS2 superconductors

Recent angle-resolved photoemission spectroscopy (ARPES) experiments have suggested that BiS2-based superconductors are at very low electron doping. Using random phase approximation (RPA) and functional renormalization group (FRG) methods, we find that g-wave pairing symmetry belonging to the irreducible representation is dominant at electron doping . The pairing symmetry is determined by inter-pocket nesting and orbital characters on the Fermi surfaces and is robust in a two-orbital model including both Hund's coupling J, and Hubbard-like Coulomb interactions U and with relatively small . With the increasing electron doping, the g-wave state competes with both the s-wave and d-wave states and no pairing symmetry emerges dominantly.

Screened Coulomb interaction calculations: cRPA implementation and applications to dynamical screening and self-consistency in uranium dioxide and cerium

We report an implementation of the constrained random phase approximation (cRPA) method within the projector augmented-wave framework. It allows for the calculation of the screened interaction in the same Wannier orbitals as our recent DFT+U and DFT+DMFT implementations. We present calculations of the dynamical Coulomb screened interaction in uranium dioxide and alpha and gamma cerium on Wannier functions. We show that a self-consistent calculation of the static screened interaction in DFT+U together with a consistent Wannier basis is mandatory for gamma cerium and uranium dioxide. We emphasize that a static approximation for the screened interaction in alpha cerium is too drastic.

Thermodynamic properties of Yb2Ti2O7pyrochlore as a function of temperature and magnetic field: Validation of a quantum spin ice exchange Hamiltonian

The thermodynamic properties of the pyrochlore Yb${}_{2}$Ti${}_{2}$O${}_{7}$ material are calculated using the numerical linked-cluster calculation method for an effective anisotropic-exchange spin-$\frac{1}{2}$ Hamiltonian with parameters recently determined by fitting the neutron scattering spin-wave data obtained at high magnetic field. Magnetization $M(T,h)$ as a function of temperature $T$ and for different magnetic fields $h$ applied along the three high-symmetry directions [100], [110], and [111] are compared with experimental measurements on the material for temperature $T>1.8$ K. The excellent agreement between experimentally measured and calculated $M(T,h)$ over the entire temperature and magnetic field ranges considered provides strong quantitative validation of the effective Hamiltonian. It also confirms that fitting the high-field neutron spin-wave spectra in the polarized paramagnetic state is an excellent method for determining the microscopic exchange constants of rare-earth insulating magnets that are described by an effective spin-$\frac{1}{2}$ Hamiltonian. Finally, we present results which demonstrate that a recent analysis of the polarized neutron scattering intensity of Yb${}_{2}$Ti${}_{2}$O${}_{7}$ using a random phase approximation method [Chang et al., Nat. Commun. 3, 992 (2012)] does not provide a good description of $M(T,h)$ for $T\ensuremath{\lesssim}10$ K, that is, in the entire temperature regime where magnetic correlations become non-negligible. With the compelling evidence that we now have at hand an accurate microscopic Hamiltonian for Yb${}_{2}$Ti${}_{2}$O${}_{7}$, our work exposes a paradox: why does this material fail to develop long-range ferromagnetic order?

Pygmy and giant electric dipole responses of medium-heavy nuclei in a self-consistent random-phase approximation approach with a finite-range interaction

The pygmy dipole resonance (PDR) is studied in various medium-heavy nuclei by using a Gogny interaction in a self-consistent Hartree-Fock plus random phase approximation method. We compare the details of the PDR structure with those of the giant dipole resonance (GDR). In the PDR protons and neutrons vibrate in phase, and the main contributions are given by particle-hole excitations involving the neutrons in excess. On the contrary, in the GDR protons and neutrons vibrate out of phase, and all the nucleons are involved in the excitation. The values of the parameters we used to define the collectivity of an excitation indicate that the PDR is less collective than the GDR. We also investigate the role of the residual interaction in the appearance of the PDR and we find a subtle interplay with the shell structure of the nucleus.

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.

Extended random phase approximation method for atomic excitation energies from correlated and variationally optimized second-order density matrices

Density matrix methods are typically ground state methods. They cannot describe excited states with the same symmetry as the ground state because they rely on energy minimization. The Random Phase Approximation (RPA) is a simple method to derive excitation energies from idempotent first-order density matrices, but the quality of the resulting excitation energies is poor. The quality of the excitation spectrum may be improved by extending the RPA to correlated states. Such an ‘extended RPA’ (ERPA) method depends only on the second-order density matrix (2DM). This work studies the main differences between the ERPA and the RPA – the influence of electron correlation, variational optimality, the ensemble nature of the density matrix and N-representability errors in the input 2DM – by applying the ERPA to exact 2DM’s and variationally optimized 2DM’s. Our findings are relevant for all methods similar to ERPA that determine excitation spectra from low-order density matrices. The inclusion of correlation makes it possible to describe the low-energy excitation spectra of the atoms He–Ne adequately, and the ERPA is thus a good starting point for further refinements, as higher-order excitations should be included to obtain chemical accuracy for many-electron systems. However, the ERPA fails for ensemble density matrices and requires a positive-definite double commutator matrix Ψ0ak†al,H,aj†aiΨ0 to guarantee that the excitation spectrum is real.

Shape transition and fluctuations in neutron-rich Cr isotopes aroundN=40

The spherical-to-prolate shape transition in neutron-rich Cr isotopes from N = 34 to 42 is studied by solving the collective Schr\"odinger equation for the five-dimensional quadrupole collective Hamiltonian. The collective potential and inertial functions are microscopically derived with use of the constrained Hartree-Fock-Bogoliubov plus local quasiparticle random-phase approximation method. Nature of the quadrupole collectivity of low-lying states is discussed by evaluating excitation spectra and electric quadrupole moments and transition strengths. The result of calculation indicates that Cr isotopes around 64Cr are prolately deformed but still possess transitional character; large-amplitude shape fluctuations dominate in their low-lying states.

Resolution-of-identity approach to Hartree–Fock, hybrid density functionals, RPA, MP2 and GW with numeric atom-centered orbital basis functions

The efficient implementation of electronic structure methods is essential for first principles modeling of molecules and solids. We present here a particularly efficient common framework for methods beyond semilocal density-functional theory (DFT), including Hartree–Fock (HF), hybrid density functionals, random-phase approximation (RPA), second-order Møller–Plesset perturbation theory (MP2) and the GW method. This computational framework allows us to use compact and accurate numeric atom-centered orbitals (NAOs), popular in many implementations of semilocal DFT, as basis functions. The essence of our framework is to employ the ‘resolution of identity (RI)’ technique to facilitate the treatment of both the two-electron Coulomb repulsion integrals (required in all these approaches) and the linear density-response function (required for RPA and GW). This is possible because these quantities can be expressed in terms of the products of single-particle basis functions, which can in turn be expanded in a set of auxiliary basis functions (ABFs). The construction of ABFs lies at the heart of the RI technique, and we propose here a simple prescription for constructing ABFs which can be applied regardless of whether the underlying radial functions have a specific analytical shape (e.g. Gaussian) or are numerically tabulated. We demonstrate the accuracy of our RI implementation for Gaussian and NAO basis functions, as well as the convergence behavior of our NAO basis sets for the above-mentioned methods. Benchmark results are presented for the ionization energies of 50 selected atoms and molecules from the G2 ion test set obtained with the GW and MP2 self-energy methods, and the G2-I atomization energies as well as the S22 molecular interaction energies obtained with the RPA method.

Failure of the random-phase-approximation correlation energy

The random phase approximation (RPA) is thought to be a successful method; however, basic errors have been found that have massive implications in the simplest molecular systems. The observed successes and failures are rationalized by examining its performance against exact conditions on the energy for fractional charges and fractional spins. Extremely simple tests reveal that the RPA method satisfies the constancy condition for fractional spins that leads to correct dissociation of closed-shell molecules and no static correlation error (such as in H${}_{2}$ dissociation) but massively fails for dissociation of odd electron systems, with an enormous delocalization error (such as H${{}_{2}}^{+}$ dissociation). Other methods related to the RPA, including the Hartree-Fock response (RPAE) or range-separated RPA, can reduce this delocalization error but only at the cost of increasing the static correlation error. None of the RPA methods have the discontinuous nature required to satisfy both exact conditions and the full unified condition (e.g., dissociation of H${{}_{2}}^{+}$ and H${}_{2}$ at the same time), emphasizing the need to go beyond differentiable energy functionals of the orbitals and eigenvalues.

Accuracy of the Faddeev random phase approximation for light atoms

The accuracy of the Faddeev random phase approximation (FRPA) method is tested by calculating the total and ionization energies of a set of light atoms up to Ar. Comparisons are made with the results of coupled-cluster singles and doubles (CCSD), third-order algebraic diagrammatic construction [ADC(3)], and with the experiment. It is seen that even for two-electron systems, He and Be-2+, the inclusion of RPA effects leads to satisfactory results and therefore it does not over-correlate the ground state. The FRPA becomes progressively better for larger atomic numbers where it gives about 5 mH more correlation energy and it shifts ionization potentials by 2-10 mH, with respect to its sister method ADC(3). The corrections for ionization potentials consistently reduce the discrepancies with the experiment.

Linear response in light deformed nuclei

We develop of a fully consistent Quasparticle Random Phase Approximation (QRPA) method that employs the canonical harmonic oscillator (HO) Hartree–Fock–Bogoliubov (HFB) basis. Skyrme energy density functionals and density–dependent pairing functionals are used for both the HFB mean field and the QRPA approaches. We accurately describe multipole strength functions in axially–symmetric deformed even–even nuclei. Isoscalar and isovector responses in the deformed 24–26Mg and 34Mg isotopes are presented investigating the consequences of neglecting the spin–orbit and Coulomb residual interactions in QRPA.

Third-order corrections to random-phase approximation correlation energies

Several random-phase approximation (RPA) correlation methods were compared in third order of perturbation theory. While all of the considered approaches are exact in second order of perturbation theory, it is found that their corresponding third-order correlation energy contributions strongly differ from the exact third-order correlation energy contribution due to missing interactions of the particle-particle-hole-hole type. Thus a simple correction method is derived which makes the different RPA methods also exact to third-order of perturbation theory. By studying the reaction energies of 16 chemical reactions for 21 small organic molecules and intermolecular interaction energies of 23 intermolecular complexes comprising weakly bound and hydrogen-bridged systems, it is found that the third-order correlation energy correction considerably improves the accuracy of RPA methods if compared to coupled-cluster singles doubles with perturbative triples as a reference.

Collective modes of a bilayer double parabolic quantum well spin polarized electron gas

AbstractWe investigate the possible electromagnetically induced collective excitation modes in a bilayer quasi‐two‐dimensional structure build from two adjacent parabolic quantum wells (PQW). We consider both charge and spin excitation modes within and beyond the random phase approximation method. To account for higher order effects we used exchange and correlation spin‐dependent local field correction factors. We analyzed intra‐ and inter‐subband excitations and provide analytic results for their excitation frequencies in the long wavelength limit. In particular, we analyze the spin polarization dependence of the lowest frequency spin density mode and show that its relevant frequency is in the hundred GHz region. (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Triaxial quadrupole deformation dynamics insd-shell nuclei aroundMg26

Large-amplitude dynamics of axial and triaxial quadrupole deformation in $^{24,26}\mathrm{Mg}$, $^{24}\mathrm{Ne}$, and $^{28}\mathrm{Si}$ is investigated on the basis of the quadrupole collective Hamiltonian constructed with the use of the constrained Hartree-Fock-Bogoliubov plus the local quasiparticle random-phase approximation method. The calculation reproduces well properties of the ground rotational bands, and $\ensuremath{\beta}$ and $\ensuremath{\gamma}$ vibrations in $^{24}\mathrm{Mg}$ and $^{28}\mathrm{Si}$. The $\ensuremath{\gamma}$ softness in the collective states of $^{26}\mathrm{Mg}$ and $^{24}\mathrm{Ne}$ are discussed. Contributions of the neutrons and protons to the transition properties are also analyzed in connection with the large-amplitude quadrupole dynamics.

Random phase approximation in a self-consistent covariant approach: recent applications

The relativistic Hartree-Fock (RHF) and Random Phase Approximation (RPA) methods are self-consistently applied to two issues of current interest. The first application is related to the isospin mixing corrections in the problem of super-allowed 0+ → 0+ β-transitions and the unitarity of the CKM matrix. The second application concerns the prediction of inclusive neutrino-nucleus cross-sections, where the results of the present model are compared with other approaches.

Electrical conductivity of plasmas of DB white dwarf atmospheres

The static electrical conductivity of non-ideal, dense, partially ionized helium plasma was calculated over a wide range of plasma parameters: temperatures $1\cdot 10^{4}\textrm{K} \lesssim T \lesssim 1\cdot 10^{5}\textrm{K}$ and mass density $1 \times 10^{-6} \textrm{g}/\textrm{cm}^{3} \lesssim \rho \lesssim 2 \textrm{g}/\textrm{cm}^{3}$. Calculations of electrical conductivity of plasma for the considered range of plasma parameters are of interest for DB white dwarf atmospheres with effective temperatures $1\cdot 10^{4}\textrm{K} \lesssim T_{eff} \lesssim 3\cdot 10^{4}\textrm{K}$. Electrical conductivity of plasma was calculated by using the modified random phase approximation and semiclassical method, adapted for the case of dense, partially ionized plasma. The results were compared with the unique existing experimental data, including the results related to the region of dense plasmas. In spite of low accuracy of the experimental data, the existing agreement with them indicates that results obtained in this paper are correct.

Random phase approximation correlation energies with exact Kohn–Sham exchange

The random phase approximation (RPA) correlation energy is expressed in terms of the exact local Kohn–Sham (KS) exchange potential and corresponding adiabatic and nonadiabatic exchange kernels for density-functional reference determinants. The approach naturally extends the RPA method in which, conventionally, only the Coulomb kernel is included. By comparison with the coupled cluster singles doubles with perturbative triples method it is shown for a set of small molecules that the new RPA method based on KS exchange yields correlation energies more accurate than RPA on the basis of Hartree–Fock exchange.

Calculation of(P,T)-odd electric dipole moments for the diamagnetic atomsX129e,Y171b,H199g,R211n, andR225a

Electric dipole moments of diamagnetic atoms of experimental interest are calculated using the relativistic Hartree-Fock and random-phase approximation methods, the many-body perturbation theory and configuration interaction technique. We consider P,T-odd interactions which give rise to atomic electric dipole moment in the second order of the perturbation theory. These include nuclear Schiff moment, P,T-odd electron-nucleon interaction and electron electric dipole moment. Interpretation of a new experimental constraint of a permanent electric dipole moment of $^{199}$Hg [W. C. Griffith {\it et al.}, Phys. Rev. Lett. {\bf 102}, 101601 (2009)] is discussed.

Self-consistent extension of random-phase approximation enlarged beyond particle-hole configurations

We present a new extension of the random-phase approximation method: the quasiboson approximation is avoided and correlations are included in the ground state without resorting to renormalized operators or renormalized matrix elements; the configuration space is enlarged by considering also elementary excitations corresponding to the annihilation of a particle (hole) and the creation of another particle (hole) on the correlated ground state, together with the particle-hole ones. Two new and relevant advantages of this method with respect to the existing extensions of random-phase approximation are highlighted: (i) the energy weighted sum rules are completely satisfied; (ii) the problem of the existence of nonphysical states in the spectrum, related to the inclusion of particle-particle and hole-hole configurations, is solved: a way to unambiguously disentangle physical from nonphysical states in the excitation spectrum is presented. The method is applied here to a three-level Lipkin model where its quality can be judged by comparing with the exact results. Both advantages (i) and (ii) shall lead to feasible future applications of this extended RPA to several realistic cases.

Quasiparticle and quasihole states of nuclei aroundNi56

The single-particle spectral function of $^{56}\mathrm{Ni}$ has been computed within the framework of self-consistent Green's functions theory. The Faddeev random phase approximation method and the $G$ matrix technique are used to account for the effects of long- and short-range physics on the spectral distribution. Large-scale calculations have been performed in spaces including up to ten oscillator shells. The chiral ${\mathrm{N}}^{3}\mathrm{LO}$ interaction is used together with a monopole correction that accounts for eventual missing three-nucleon forces. The single-particle energies associated with nucleon transfer to valence $1p0f$ orbits are found to be almost converged with respect to both the size of the model space and the oscillator frequency. The results support that $^{56}\mathrm{Ni}$ is a good doubly magic nucleus. The absolute spectroscopic factors to the valence states on $A=55,57$ are also obtained. For the transition between the ground states of $^{57}\mathrm{Ni}$ and $^{56}\mathrm{Ni}$, the calculations nicely agree with heavy-ion knockout experiments.