Random Phase Approximation Calculations Research Articles

Ab initio description of monopole resonances in light- and medium-mass nuclei

The paper is the third of a series dedicated to the ab initio description of monopole giant resonances in mid-mass closed- and open-shell nuclei via the so-called projected generator coordinate method. The present focus is on the computation of the moments mk\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$m_k$$\\end{document} of the monopole strength distribution, which are used to quantify its centroid energy and dispersion. First, the capacity to compute low-order moments via two different methods is developed and benchmarked for the m1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$m_1$$\\end{document} moment. Second, the impact of the angular momentum projection on the centroid energy and dispersion of the monopole strength is analysed before comparing the results to those obtained from consistent quasi-particle random phase approximation calculations. Next, the so-called energy weighted sum rule (EWSR) is investigated. First, the appropriate ESWR in the center-of-mass frame is derived analytically. Second, the intrinsic EWSR is tested in order to quantify the (unwanted) local-gauge symmetry breaking of the presently employed chiral effective field theory (χ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\chi $$\\end{document}EFT) interactions. Finally, the infinite nuclear matter incompressibility associated with the employed χ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\chi $$\\end{document}EFT interactions is extracted by extrapolating the finite-nucleus incompressibility computed from the monopole centroid energy.

Structural phase transition, s±-wave pairing, and magnetic stripe order in bilayered superconductor La3Ni2O7 under pressure

Motivated by the recently discovered high-Tc superconductor La3Ni2O7, we comprehensively study this system using density functional theory and random phase approximation calculations. At low pressures, the Amam phase is stable, containing the Y2− mode distortion from the Fmmm phase, while the Fmmm phase is unstable. Because of small differences in enthalpy and a considerable Y2− mode amplitude, the two phases may coexist in the range between 10.6 and 14 GPa, beyond which the Fmmm phase dominates. In addition, the magnetic stripe-type spin order with wavevector (π, 0) was stable at the intermediate region. Pairing is induced in the s±-wave channel due to partial nesting between the M = (π, π) centered pockets and portions of the Fermi surface centered at the X = (π, 0) and Y = (0, π) points. This resembles results for iron-based superconductors but has a fundamental difference with iron pnictides and selenides. Moreover, our present efforts also suggest La3Ni2O7 is qualitatively different from infinite-layer nickelates and cuprate superconductors.

Accurate Excitation Energies of Point Defects from Fast Particle-Particle Random Phase Approximation Calculations.

We present an efficient particle-particle random phase approximation (ppRPA) approach that predicts accurate excitation energies of point defects, including the nitrogen-vacancy (NV-) and silicon-vacancy (SiV0) centers in diamond and the divacancy center (VV0) in 4H silicon carbide, with errors of ±0.2 eV compared with experimental values. Starting from the (N + 2)-electron ground state calculated with density functional theory (DFT), the ppRPA excitation energies of the N-electron system are calculated as the differences between the two-electron removal energies of the (N + 2)-electron system. We demonstrate that the ppRPA excitation energies converge rapidly with a few hundred canonical active-space orbitals. We also show that active-space ppRPA has weak DFT starting-point dependence and is significantly cheaper than the corresponding ground-state DFT calculation. This work establishes ppRPA as an accurate and low-cost tool for investigating excited-state properties of point defects and opens up new opportunities for applications of ppRPA to periodic bulk materials.

Nb3Cl8: a prototypical layered Mott-Hubbard insulator

Despite its simplicity and relevance for the description of electronic correlations in solids, the Hubbard model is seldom inarguably realized in real materials. Here, we show that monolayer Nb3Cl8 is an ideal candidate to be described within a single-orbital Hubbard model, constructed within a “molecular” rather than atomic basis set using ab initio constrained random phase approximation calculations. We provide the necessary ingredients to connect experimental reality with ab initio material descriptions and correlated electron theory, which clarifies that monolayer Nb3Cl8 is a Mott insulator with a gap of about 1.4 to 2.0 eV depending on its dielectric environment. Comparisons to an atomistic three-orbital model show that the single-molecular-orbital description is adequate and reliable. We further comment on the electronic and magnetic structure of the compound and show that the Mott insulating state survives in the low-temperature bulk phases of the material featuring distinct experimentally verifiable characteristics.

Towards systematic large scale Quasiparticle Random-Phase Approximation calculations with covariant and chiral interactions

Towards systematic large scale Quasiparticle Random-Phase Approximation calculations with covariant and chiral interactions

Introducing the embedded random phase approximation: H2 dissociative adsorption on Cu(111) as an exemplar

The random phase approximation (RPA) as a means of treating electron correlation recently has been shown to outperform standard density functional theory (DFT) approximations in a variety of cases. However, the computational cost of the RPA is substantially more than DFT, especially when aiming to study extended surfaces. Properly accounting for sufficient surface ensemble size, Brillouin zone sampling, and vacuum separation of periodic images in standard periodic-planewave-based DFT code raises the cost to achieve converged results. Here, we show that sub-system embedding schemes enable use of the RPA for modeling heterogeneous reactions at reduced computational cost. We explore two different embedded RPA (emb-RPA) approaches, periodic emb-RPA and cluster emb-RPA. We use the (experimentally and theoretically) well-studied H2 dissociative adsorption on Cu(111) as our exemplar, and first perform full periodic RPA calculations as a benchmark. The full RPA results match well the semi-empirical barrier fit to experimental observables and others derived from high-level computations, e.g., from recent embedded n-electron valence second order perturbation theory [Zhao et al., J. Chem. Theory Comput. 16(11), 7078–7088 (2020)] and quantum Monte Carlo [Doblhoff-Dier et al., J. Chem. Theory Comput. 13(7), 3208–3219 (2017)] simulations. Among the two emb-RPA approaches tested, the cluster emb-RPA accurately reproduces the energy profile (maximum error of 50 meV along the reaction pathway) while reducing the computational cost by approximately two orders of magnitude. We therefore expect that the embedded cluster approach will enable wider RPA implementation in heterogeneous catalysis.

Basis-Set-Error-Free Random-Phase Approximation Correlation Energies for Atoms Based on the Sternheimer Equation.

The finite basis set errors for all-electron random-phase approximation (RPA) correlation energy calculations are analyzed for isolated atomic systems. We show that, within the resolution-of-identity (RI) RPA framework, the major source of the basis set errors is the incompleteness of the single-particle atomic orbitals used to expand the Kohn-Sham eigenstates, instead of the auxiliary basis set (ABS) to represent the density response function χ0 and the bare Coulomb operator v. By solving the Sternheimer equation for the first-order wave function on a dense radial grid, we are able to eliminate the major error─the incompleteness error of the single-particle atomic basis set─for atomic RPA calculations. The error stemming from a finite ABS can be readily rendered vanishingly small by increasing the size of the ABS, or by iteratively determining the eigenmodes of the χ0v operator. The variational property of the RI-RPA correlation energy can be further exploited to optimize the ABS in order to achieve fast convergence of the RI-RPA correlation energy. These numerical techniques enable us to obtain basis-set-error-free RPA correlation energies for atoms, and in this work, such energies for atoms from H to Kr are presented. The implications of the numerical techniques developed in the present work for addressing the basis set issue for molecules and solids are discussed.

Evaluations of uncertainties in simulations of propagation of ultrahigh-energy cosmic-ray nuclei derived from microscopic nuclear models

Photodisintegration is a main energy loss process for ultrahigh-energy cosmic-ray (UHECR) nuclei in intergalactic space. Therefore, it is crucial to understand systematic uncertainty in photodisintegration when simulating the propagation of UHECR nuclei. In this work, we calculated the cross sections using the random phase approximation (RPA) of density functional theory (DFT), a microscopic nuclear model. We calculated the E1 strength of 29 nuclei using three different density functionals. We obtained the cross sections of photonuclear reactions, including photodisintegration, with the E1 strength. Then, we implemented the cross sections in the cosmic-ray propagation code CRPropa. We found that assuming certain astrophysical parameter values, the difference between UHECR energy spectrum predictions using the RPA calculation and the default photodisintegration model in CRPropa can be more than the statistical uncertainty of the spectrum. We also found that the differences between the RPA calculations and CRPropa default in certain astrophysical parameters obtained by a combined fit of UHECR energy spectrum and composition data assuming a phenomenological model of UHECR sources can be more than the uncertainty of the data.

Photon strength functions, level densities, and isomeric ratio in Er168 from the radiative neutron capture measured at the DANCE facility

Background: The statistical approach is usually applied for the description of electromagnetic decay of the nucleus with the exception of the lowest excitation energies as well as for the calculation of the interaction of photons with nuclei, in particular the reaction cross sections. This concept employs nuclear level density (NLD) and photon strength functions (PSFs).Purpose: While PSFs and NLD of some well-deformed rare-earth nuclei were measured by several methods, sometimes with conflicting results, the PSFs of $^{168}\mathrm{Er}$ were addressed only by $(\ensuremath{\gamma},{\ensuremath{\gamma}}^{\ensuremath{'}})$ experiments. On the other hand, the low-lying levels of $^{168}\mathrm{Er}$ are well studied, including the isomeric state at 1094 keV, which enables various tests of the statistical approach.Methods: The $\ensuremath{\gamma}$ rays following radiative neutron capture on a $^{167}\mathrm{Er}$ sample were measured with the highly segmented $\ensuremath{\gamma}$-ray calorimeter Detector for Advanced Neutron Capture Experiments at the Los Alamos Neutron Science Center. The $\ensuremath{\gamma}$-ray energy spectra for different multiplicities (multistep cascade, or MSC, spectra) were gathered for many $s$-wave resonances of both possible spins. Moreover, we were able to detect the decay of the short-lived isomer and deduce the isomeric ratio for a few resonances.Results: Analysis of the MSC spectra within the statistical model enabled us to draw conclusions about dipole PSFs, in particular on the properties of the scissors mode, and NLD. The spectra can be well reproduced with phenomenological PSFs models but not with any of several models based on quasiparticle random-phase approximation (QRPA) calculations with different interactions. We showed that nonstatistical effects in feeding of the isomeric state play a role up to excitation energies of at least about 2 MeV.Conclusions: Deduced parameters of the scissors mode were found to be similar to those of neighbor well-deformed even-even Gd and Dy nuclei. Models like that of Kadmenskij, Markushev, and Furman (KMF) or like the modified generalized Lorentzian (MGLO) model provide a good description of experimental spectra. In contrast to several previous analyses of well-deformed rare-earth isotopes, we were able to match the experimental isomeric ratio with statistical model simulations.

Nuclear magnetic moment of the neutron-rich nucleus O21

The ground-state magnetic dipole moment of the neutron-rich $^{21}\mathrm{O}$ isotope has been measured via $\ensuremath{\beta}$-ray-detected nuclear magnetic resonance ($\ensuremath{\beta}\text{\ensuremath{-}}\mathrm{NMR}$) spectroscopy by using a spin-polarized secondary beam of $^{21}\mathrm{O}$ produced from the $^{22}\mathrm{Ne}$ primary beam. From the present measurement, the $g$ factor $|{g}_{\mathrm{exp}}(^{21}\mathrm{O}_{\mathrm{g}.\mathrm{s}.})|=0.6036(14)$ has been determined. Based on the comparison of this value with Schmidt values, we unambiguously confirm the $\ensuremath{\nu}{d}_{5/2}$ configuration with spin and parity assignments ${I}^{\ensuremath{\pi}}=5/{2}^{+}$ for the $^{21}\mathrm{O}$ ground state, suggested by previously reported studies. Consequently, the magnetic moment has been determined as ${\ensuremath{\mu}}_{\mathrm{exp}}(^{21}\mathrm{O}_{\mathrm{g}.\mathrm{s}.})=(\ensuremath{-})1.5090(35){\ensuremath{\mu}}_{N}$. The obtained experimental magnetic moment is in good agreement with the predictions of the shell-model calculations using the USD, YSOX, and SDPF-M interactions as well as random phase approximation (RPA) calculations. This observation indicates that the $^{21}\mathrm{O}$ nucleus in its ground state does not manifest any anomalous structure and is not influenced by the proximity of the drip line.

Low-energy plasmon excitations in infinite-layer nickelates

The discovery of superconductivity in infinite-layer nickelates is presently an important topic in condensed-matter physics, and potential similarities to and differences from cuprates are under intense debate. We determine general features of the charge excitation spectrum in nickelates from two opposite viewpoints: (i) Nickelates are regarded as strongly correlated electron systems like cuprate superconductors and thus can be described by the $t\text{\ensuremath{-}}J$ model, and (ii) electron correlation effects are not as strong as in cuprates, and thus, random-phase approximation (RPA) calculations may capture the essential physics. We find that in both cases, plasmon excitations are realized around the momentum transfer $\mathbf{q}=(0,0,{q}_{z})$, although they tend to be damped more strongly in the RPA. In particular, this damping is enhanced by the relatively large interlayer hopping expected in nickelates. Besides reproducing the optical plasmon at $\mathbf{q}=(0,0,0)$ observed in ${\mathrm{Nd}}_{0.8}{\mathrm{Sr}}_{0.2}{\mathrm{NiO}}_{2}$, we obtain low-energy plasmons with gaps of $\ensuremath{\sim}360$ and $\ensuremath{\sim}560$ meV at $\mathbf{q}=(0,0,{q}_{z})$ for finite ${q}_{z}$ in cases (i) and (ii), respectively. The present work offers a possible theoretical hint to answer whether nickelates are cupratelike or not and contributes to the general understanding of the charge dynamics in nickelates.

Propagating charge carrier plasmons in Sr2RuO4

We report on studies of charge carrier plasmon excitations in ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}$ by transmission electron energy-loss spectroscopy. In particular, we present results on the plasmon dispersion and its width as a function of momentum transfer. The dispersion can be qualitatively explained in the framework of random phase approximation calculations, using an unrenormalized tight-binding band structure. The constant long-wavelength width of the plasmon indicates that it is caused by a decay into interband transitions and not by quantum critical fluctuations. The results from these studies on a prototypical correlated metal system show that the long-wavelength plasmon excitations near 1 eV are caused by resilient quasiparticles and are not influenced by correlation effects.

Study of the Nuclear Structure for Some Nuclei Using Self-Consistent RPA Calculations with Skyrme-Type Interaction

In the present research, some static and dynamic nuclear properties of the closed-shell nuclei; 58Ni, 90Zr, 116Sn, and 144Sm nuclei have been studied using the Random Phase Approximation (RPA) method framework and different Skyrme parameterizations, particularly SyO-, Sk255, SyO+, SLy4, BSk17, and SLy5. In particular, in studies of static properties such as nuclear densities for neutrons, protons, mass, and charge densities with their corresponding rms radii, the single-particle nuclear density distributions All the obtained results agreed well with the relevant experimental data. Concerning the dynamic properties, the excitation energy, transition density, and giant resonance modes for the excitation to the low-lying negative partite excited states 1–, 3–, 5–, and 7– have also been studied. The findings indicate that estimates of RPA with Skyrme-type interactions are a good way to describe the properties of the structure of even-even, closed-shell nuclei.

Heat capacity double transitions in time-reversal symmetry broken superconductors

Standard superconductors display a ubiquitous discontinuous jump in the electronic specific heat at the critical superconducting transition temperature. In a growing class of unconventional superconductors, however, a second order parameter component may get stabilized and produce a second heat capacity jump at a lower temperature, typically associated with the spontaneous breaking of time-reversal symmetry. The splitting of the two specific heat discontinuities can be controlled by external perturbations such as chemical substitution, hydrostatic pressure, or uniaxial strain. We develop a theoretical quantitative multi-band framework to determine the ratio of the heat capacity jumps, given the band structure and the order parameter momentum structure. We discuss the conditions of the gap profile which determine the amplitude of the second jump. We apply our formalism to the case of Sr$_2$RuO$_4$, and using the gap functions from a microscopic random phase approximation calculation, we show that recently-proposed accidentally degenerate order parameters may exhibit a strongly suppressed second heat capacity jump. We discuss the origin of this result and consider also the role of spatial inhomogeneity on the specific heat. Our results provide a possible explanation of why a second heat capacity jump has so far evaded experimental detection in Sr$_2$RuO$_4$.

Crossing N=28 Toward the Neutron Drip Line: First Measurement of Half-Lives at FRIB

New half-lives for exotic isotopes approaching the neutron drip-line in the vicinity of N∼28 for Z=12-15 were measured at the Facility for Rare Isotope Beams (FRIB) with the FRIB decay station initiator. The first experimental results are compared to the latest quasiparticle random phase approximation and shell-model calculations. Overall, the measured half-lives are consistent with the available theoretical descriptions and suggest a well-developed region of deformation below ^{48}Ca in the N=28 isotones. The erosion of the Z=14 subshell closure in Si is experimentally confirmed at N=28, and a reduction in the ^{38}Mg half-life is observed as compared with its isotopic neighbors, which does not seem to be predicted well based on the decay energy and deformation trends. This highlights the need for both additional data in this very exotic region, and for more advanced theoretical efforts.

Accurately Determining the Phase Transition Temperature of CsPbI3 via Random-Phase Approximation Calculations and Phase-Transferable Machine Learning Potentials

While metal halide perovskites (MHPs) have shown great potential for various optoelectronic applications, their widespread adoption in commercial photovoltaic cells or photosensors is currently restricted, given that MHPs such as CsPbI3 and FAPbI3 spontaneously transition to an optically inactive nonperovskite phase at ambient conditions. Herein, we put forward an accurate first-principles procedure to obtain fundamental insight into this phase stability conundrum. To this end, we computationally predict the Helmholtz free energy, composed of the electronic ground state energy and thermal corrections, as this is the fundamental quantity describing the phase stability in polymorphic materials. By adopting the random phase approximation method as a wave function-based method that intrinsically accounts for many-body electron correlation effects as a benchmark for the ground state energy, we validate the performance of different exchange-correlation functionals and dispersion methods. The thermal corrections, accessed through the vibrational density of states, are accessed through molecular dynamics simulations, using a phase-transferable machine learning potential to accurately account for the MHPs’ anharmonicity and mitigate size effects. The here proposed procedure is critically validated on CsPbI3, which is a challenging material as its phase stability changes slowly with varying temperature. We demonstrate that our procedure is essential to reproduce the experimental transition temperature, as choosing an inadequate functional can easily miss the transition temperature by more than 100 K. These results demonstrate that the here validated methodology is ideally suited to understand how factors such as strain engineering, surface functionalization, or compositional engineering could help to phase-stabilize MHPs for targeted applications.

Low-energy monopole strength in spherical and axially deformed nuclei: Cluster and soft modes

Background: Several recent experiments report significant low-energy isoscalar monopole strength, below the giant resonance, in various nuclei. In light $\ensuremath{\alpha}$-conjugate nuclei, these low-energy resonances were recently interpreted as cluster vibration modes. However, the nature of these excitations in neutron-rich nuclei remains elusive.Purpose: The present work provides a systematic analysis of the low-energy monopole strength in isotopic chains, from neon to germanium, in order to monitor and understand its nature and conditions of emergence.Methods: We perform covariant quasiparticle random phase approximation calculations, formulated within the finite amplitude method, on top of constrained relativistic Hartree-Bogoliubov (RHB) reference states.Results: Neutron excess leads to the appearance of low-energy excitations according to a systematic pattern reflecting the single-particle features of the underlying RHB reference state. With the onset of deformation, these low-energy resonances get split and give rise to more complex patterns, with possible mixing with the giant resonance. At lower energy, clusterlike excitations found in $N=Z$ systems survive in neutron-rich nuclei, with valence neutrons arranging in molecularlike orbitals. Finally, at very low energy, pair excitations are also found in superfluid nuclei, but remain negligible in most of the cases.Conclusions: The low-energy part of the monopole strength exhibits various modes, from cluster vibrations ($\ensuremath{\approx}$5--10 MeV) to components of the giant resonance downshifted by the onset of deformation, including soft modes ($\ensuremath{\approx}$10--15 MeV) as well as pair excitation ($<$5 MeV), with possible mixing, depending on neutron excess, deformation, and pairing energy.

Mean field versus random-phase approximation calculation of the energy of an impurity immersed in a spin-1/2 superfluid

In this article we calculate the energy of an impurity weakly coupled to a spin 1/2 fermionic superfluid. We show that the divergences resulting from three-body physics can only be cured using a proper description of the excitations of the many-body background. We highlight the crucial role played by interactions between quasiparticles which are overlooked within BCS (Bardeen-Cooper-Schrieffer) mean-field theory of fermionic superfluidity. By contrast, we prove that their addition using the Random Phase Approximation (RPA) allows us to regularize the energy of the impurity. Finally, we show that these beyond mean-field corrections should be observable by the analysis of the frequency shift of the impurity center of mass oscillations in an external confining potential.

Phase transitions of zirconia: Machine-learned force fields beyond density functional theory

We present an approach to generate machine-learned force fields (MLFF) with beyond density functional theory (DFT) accuracy. Our approach combines on-the-fly active learning and $\Delta$-machine learning in order to generate an MLFF for zirconia based on the random phase approximation (RPA). Specifically, an MLFF trained on-the-fly during DFT based molecular dynamics simulations is corrected by another MLFF that is trained on the differences between RPA and DFT calculated energies, forces and stress tensors. Thanks to the relatively smooth nature of the differences, the expensive RPA calculations are performed only on a small number of representative structures of small unit cells. These structures are determined by a singular value decomposition rank compression of the kernel matrix with low spatial resolution. This dramatically reduces the computational cost and allows us to generate an MLFF fully capable of reproducing high-level quantum-mechanical calculations beyond DFT. We carefully validate our approach and demonstrate its success in studying the phase transitions of zirconia.

Staggered Mesh Method for Correlation Energy Calculations of Solids: Random Phase Approximation in Direct Ring Coupled Cluster Doubles and Adiabatic Connection Formalisms

We propose a staggered mesh method for correlation energy calculations of periodic systems under the random phase approximation (RPA), which generalizes the recently developed staggered mesh method for periodic second order Møller-Plesset perturbation theory (MP2) calculations [Xing; Li; Lin J. Chem. Theory Comput. 2021]. Compared to standard RPA calculations, the staggered mesh method introduces negligible additional computational cost. It avoids a significant portion of the finite-size error and can be asymptotically advantageous for quasi-1D systems and certain quasi-2D and 3D systems with high symmetries. We demonstrate the applicability of the method using two different formalisms: the direct ring coupled cluster doubles (drCCD) theory, and the adiabatic-connection (AC) fluctuation-dissipation theory. In the drCCD formalism, the second order screened exchange (SOSEX) correction can also be readily obtained using the staggered mesh method. In the AC formalism, the staggered mesh method naturally avoids the need of performing "head/wing" corrections to the dielectric operator. The effectiveness of the staggered mesh method for insulating systems is theoretically justified by investigating the finite-size error of each individual perturbative term in the RPA correlation energy, expanded as an infinite series of terms associated with ring diagrams. As a side contribution, our analysis provides proof that the finite-size error of each perturbative term of standard RPA and SOSEX calculations scales as , where Nk is the number of grid points in a Monkhorst-Pack mesh.