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Quasiparticle-random-phase approximation treatment of the transverse wobbling mode reconsidered
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Implementation of the continuum random phase approximation model in the GENIE generator and an analysis of nuclear effects in low-energy transfer neutrino interactions
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Photoionization cross sections for atomic chlorine using an open-shell random-phase approximation
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Cubic-scaling algorithm and self-consistent mean field for random-phase approximation with second-order screened exchange.
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Cubic-scaling algorithm and self-consistent mean field for the random-phase approximation with second-order screened exchange.
Abstract not provided.
Autoionization resonances in the photoabsorption spectra of Fe{sup n+} iron ions
The photoabsorption cross sections of a neutral iron atom, as well as positive Fe{sup +} and Fe{sup 2+} ions, are calculated in the relativistic random-phase approximation with exchange in the energy range 20–160 eV. The wavefunctions of the ground and excited states are calculated in the single-configuration Hartree–Fock–Dirac approximation. The resultant photoabsorption spectra are compared with experimental data and with the results of calculations based on the nonrelativistic spin-polarized version of the random-phase approximation with exchange. Series of autoionization resonance peaks, as well as giant autoionization resonance lines corresponding to discrete transitions 3p → 3d, are clearly observed in the photoabsorption cross sections. The conformity of the positions of calculated peaks of giant autoionization resonances with experimental data is substantially improved by taking into account additionally the correlation electron–electron interaction based on the model of the dynamic polarization potential.
Magnon–magnon interactions in O(3) ferromagnets and equations of motion for spin operators
The method of equations of motion for spin operators in the case of O(3) Heisenberg ferromagnet is systematically analyzed starting from the effective Lagrangian. It is shown that the random phase approximation and the Callen approximation can be understood in terms of perturbation theory for type B magnons. Also, the second order approximation of Kondo and Yamaji for one dimensional ferromagnet is reduced to the perturbation theory for type A magnons. An emphasis is put on the physical picture, i.e. on magnon–magnon interactions and symmetries of the Heisenberg model. Calculations demonstrate that all three approximations differ in manner in which the magnon–magnon interactions arising from the Wess–Zumino term are treated, from where specific features and limitations of each of them can be deduced.
Magnetic order and spin excitations in the Kitaev–Heisenberg model on a honeycomb lattice
We consider the quasi-two-dimensional pseudo-spin-1/2 Kitaev–Heisenberg model proposed for A{sub 2}IrO{sub 3} (A = Li, Na) compounds. The spin-wave excitation spectrum, the sublattice magnetization, and the transition temperatures are calculated in the random phase approximation for four different ordered phases observed in the parameter space of the model: antiferromagnetic, stripe, ferromagnetic, and zigzag phases. The Néel temperature and temperature dependence of the sublattice magnetization are compared with the experimental data on Na{sub 2}IrO{sub 3}.
Explicitly correlated ring-coupled-cluster-doubles theory
The connection between the random-phase approximation and the ring-coupled-cluster-doubles method bridges the gap between density-functional and wave-function theories and the importance of the random-phase approximation lies in both its broad applicability and this linking role in electronic-structure theory. In this contribution, we present an explicitly correlated approach to the random-phase approximation, based on the direct ring-coupled-cluster-doubles ansatz, which overcomes the problem of slow basis-set convergence, inherent to the random-phase approximation. Benchmark results for a test set of 106 molecules and a selection of 10 organic complexes from the S22 test set demonstrate that convergence to within 99% of the basis-set limit is reached for triple-zeta basis sets for atomisation energies, while quadruple-zeta basis sets are required for interaction energies. Corrections due to single excitations into the complementary auxiliary space reduce the basis-set incompleteness error by one order of magnitude, while contributions due to the coupling of conventional and geminal amplitudes are in general negligible. We find that a non-iterative explicitly correlated correction to first order in perturbation theory exhibits the best ratio of accuracy to computational cost.
Role of polarization interaction in photoionization of negative ions of alkali metals
Photoionization processes of negative ions of sodium, potassium, and rubidium were investigated. Calculations of the dependence of the photoionization cross section on the photon energy were performed within the Random Phase Approximation with Exchange for outer subshells (RPAE) and within the Generalized Random Phase Approximation with Exchange (GRPAE) for inner subshells. The latter theoretical approach includes both many-electron correlations and core rearrangement due to escape of one of the electrons from the system. The results of calculations for the negative sodium ion were found to be in good agreement with experimental data. Better agreement was achieved by allowing dynamical polarization of the electron core. It manifests itself as a many-electron response to variation of the external electromagnetic field, which results from the excitation of the many-electron system. Detailed study of the main mechanisms determining the cross section dependence profile was carried out. These mechanisms are the inter- and intrachannel correlations acting as a many-electron response to the external field, the electron core rearrangement, and the dynamic polarization. Besides sodium and potassium ions, photoionization of rubidium ion was investigated. A new method accounting for polarization corrections to optical transition amplitudes based on combination of the Dyson equation and RPAE is proposed.
General trends of superconducting pairing and magnetic correlations in the Ruddlesden-Popper nickelate 𝑚-layered superconductors La 𝑚+1 Ni 𝑚 O 3𝑚+1
Here, we report a comprehensive theoretical analysis of the Ruddlesden-Popper layered nickelates La 𝑚+1 Ni 𝑚 O 3𝑚+1 (𝑚 = 1 to 6) under pressure. These materials have recently received significant attention due to the discovery of superconductivity in some nickelates under pressure. Our results suggest that, while these Ruddlesden-Popper layered nickelates display many similarities, they also show noticeable differences. One of the common features of La 𝑚+1 Ni 𝑚 O 3𝑚+1 is that the electronic states near the Fermi level are mainly contributed by Ni 3𝑑 orbitals, slightly hybridized with O 2𝑝 orbitals. The Ni 𝑑 3𝑧 2 −𝑟 2 orbitals display bonding-antibonding, or bonding-antibonding-nonbonding, characteristic splittings, depending on the even or odd number of stacking layers 𝑚. In addition, the ratio of the in-plane interorbital hopping between 𝑑 3𝑧 2 −𝑟 2 and 𝑑 𝑥 2 −𝑦 2 orbitals and in-plane intraorbital hopping between 𝑑 𝑥 2 −𝑦 2 orbitals was found to be large in La 𝑚+1 Ni 𝑚 O 3𝑚+1 (𝑚 = 1 to 6), and this ratio increases from 𝑚 = 1 to 𝑚 = 6, suggesting that the in-plane hybridization will increase as the layer number 𝑚 increases. In contrast to the dominant 𝑠 ± -wave state driven by spin fluctuations in the bilayer La 3 Ni 2 O 7 and trilayer La 4 Ni 3 O 10 , two nearly degenerate 𝑑 𝑥 2 −𝑦 2 -wave and 𝑠 ± -wave leading states were obtained in the four-layer stacking La 5 Ni 4 O 13 and five-layer stacking La 6 Ni 5 O 16 . The leading 𝑠 ± -wave state was recovered in the six-layer material La 7 Ni 6 O 19 with slightly higher calculated pairing strength 𝜆 than that of the 𝑑 𝑥 2 −𝑦 2 -wave state. All this evidence suggests that both 𝑠 ± -wave and 𝑑 𝑥 2 −𝑦 2 -wave channels are strongly competing in the high-order niceklates based on our random-phase approximation calculations. In general, at the level of the random-phase approximation treatment, the superconducting transition temperature 𝑇 𝑐 decreases in stoichiometric bulk systems from the bilayer La 3 Ni 2 O 7 to the six-layer La 7 Ni 6 O 19 , despite the 𝑚-dependent dominant pairing. Both in-plane and out-of-plane magnetic correlations are found to be quite complex. Within the in-plane direction, we obtained the peak of the magnetic susceptibility at 𝐪 = (0.6𝜋, 0.6𝜋) for La 5 Ni 4 O 13 (𝑚 = 4) and La 7 Ni 6 O 19 (𝑚 = 6) and at 𝐪 = (0.7𝜋, 0.7𝜋) for La 6 Ni 5 O 16 (𝑚 = 5). Along the out-of-plane direction, four layers are coupled as ↓−↑−↑−↓ in La 5 Ni 4 O 13 , five layers are coupled as ↑−↑−↓−↑−↑ in La 6 Ni 5 O 16 , and six layers are coupled as ↑−↓−↓−↑−↑−↓ in La 7 Ni 6 O 19 .
Conical Intersections from Particle–Particle Random Phase and Tamm–Dancoff Approximations
The particle–particle random phase approximation (pp-RPA) and the particle–particle Tamm–Dancoff approximation (pp-TDA) are applied to the challenging conical intersection problem. Because they describe the ground and excited states on the same footing and naturally take into account the interstate interaction, these particle–particle methods, especially the pp-TDA, can correctly predict the dimensionality of the conical intersection seam as well as describe the potential energy surface in the vicinity of conical intersections. Though the bond length of conical intersections is slightly underestimated compared with the complete-active-space self-consistent field (CASSCF) theory, the efficient particle–particle methods are promising for conical intersections and nonadiabatic dynamics.
Sublinear scaling for time-dependent stochastic density functional theory
A stochastic approach to time-dependent density functional theory is developed for computing the absorption cross section and the random phase approximation (RPA) correlation energy. The core idea of the approach involves time-propagation of a small set of stochastic orbitals which are first projected on the occupied space and then propagated in time according to the time-dependent Kohn-Sham equations. The evolving electron density is exactly represented when the number of random orbitals is infinite, but even a small number (≈16) of such orbitals is enough to obtain meaningful results for absorption spectrum and the RPA correlation energy per electron. We implement the approach for silicon nanocrystals using real-space grids and find that the overall scaling of the algorithm is sublinear with computational time and memory.
Fractional charge and spin errors in self-consistent Green’s function theory
We examine fractional charge and spin errors in self-consistent Green’s function theory within a second-order approximation (GF2). For GF2, it is known that the summation of diagrams resulting from the self-consistent solution of the Dyson equation removes the divergences pathological to second-order Møller-Plesset (MP2) theory for strong correlations. In the language often used in density functional theory contexts, this means GF2 has a greatly reduced fractional spin error relative to MP2. The natural question then is what effect, if any, does the Dyson summation have on the fractional charge error in GF2? To this end, we generalize our previous implementation of GF2 to open-shell systems and analyze its fractional spin and charge errors. We find that like MP2, GF2 possesses only a very small fractional charge error, and consequently minimal many electron self-interaction error. This shows that GF2 improves on the critical failings of MP2, but without altering the positive features that make it desirable. Furthermore, we find that GF2 has both less fractional charge and fractional spin errors than typical hybrid density functionals as well as random phase approximation with exchange.
Effects of quasiparticle-vibration coupling on Gamow-Teller strength and 𝛽 decay with the Skyrme proton-neutron finite-amplitude method
We adapt the proton-neutron finite-amplitude method, which in its original form is an efficient implementation of the Skyrme quasiparticle random phase approximation, to include the coupling of quasiparticles to like-particle phonons. The approach allows us to add beyond-quasiparticle random-phase approximation correlations to computations of Gamow-Teller strength and 𝛽-decay rates in deformed nuclei for the first time. We test the approach in several deformed isotopes for which measured strength distributions are available. Furthermore, the additional correlations dramatically improve agreement with the data, and will lead to improved global 𝛽-decay rates.
Coupled Hubbard ladders at weak coupling: Pairing and spin excitations
The Hubbard model provides a simple framework in which one can study how certain aspects of the electronic structure of strongly interacting systems can be tuned to optimize the superconducting pairing correlations and how these changes affect the mechanisms giving rise to them. Here we use a weak-coupling random phase approximation to study a two-dimensional Hubbard model with a unidirectional modulation of the hopping amplitudes as the system evolves from the uniform square lattice to an array of weakly coupled two-leg ladders. We find that the pairing correlations retain their dominant d x 2 - y 2- wavelike structure and that they are significantly enhanced for a slightly modulated lattice. This enhancement is traced backed to an increase in the strength of the spin-fluctuation pairing interaction due to favorable Fermi surface nesting in the modulated system. We then use a random-phase approximation BCS framework to examine the evolution of the neutron resonance in the superconducting state. We find that it changes only weakly for moderate modulations, but breaks up into two distinct resonances at incommensurate wave vectors in the limit of weakly coupled ladders.