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The random-phase approximation (RPA) as an approach for computing the electronic correlation energy is reviewed. After a brief account of its basic concept and historical development, the paper is devoted to the theoretical formulations of…
We present an extension of the random--phase approximation (RPA) where the RPA phonons are used as building blocks to construct the excited states. In our model, that we call double RPA (DRPA), we include up to two RPA phonons. This is an…
We recently demonstrated a connection between the random phase approximation (RPA) and coupled cluster theory [J. Chem. Phys. 129, 231101 (2008)]. Based on this result, we here propose and test a simple scheme for introducing long-range RPA…
We present a study of the equilibrium properties of $sp$-bonded solids within the pseudopotential approach, employing recently proposed generalized gradient approximation (GGA) exchange correlation functionals. We analyze the effects of the…
We present an approximation scheme of the nonperturbative renormalization group that preserves the momentum dependence of correlation functions. This approximation scheme can be seen as a simple improvement of the local potential…
Anderson localization has been studied extensively for more than half a century. However, while our understanding has been greatly enhanced by calculations based on a small epsilon expansion in d = 2 + epsilon dimensions in the framework of…
Antiferromagnetic or charge density wave fluctuations couple with light through the recently discovered {\pi}-ton contribution to the optical conductivity, and quite generically constitute the dominant vertex corrections in low-dimensional…
The inelastic scattering rates of quasiparticles in a two-dimensional d-wave superconductor, which arise from interactions with either acoustic phonons or other quasiparticles, are calculated within second order perturbation theory. We…
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…
A systematic analysis of giant quadrupole resonances is performed for several nuclei, from $^{30}$Si to $^{208}$Pb, within the subtracted second random--phase--approximation (SSRPA) model in the framework of the energy--density--functional…
In the present article, we introduce the relativistic Cholesky-decomposed density (CDD) matrix second-order M{\o}ller-Plesset perturbation theory (MP2) energies. The working equations are formulated in terms of the usual intermediates of…
We performed the multipole decomposition analysis (MDA) for the ${}^{208}{\rm Pb}(p,n)$ data in order to obtain the spin-dipole (SD) strengths separated into each $\Delta J^{\pi}$ contribution $dB({\rm SD}_{\Delta J^{\pi}};\omega)/d\omega$.…
Detrended fluctuation analysis (DFA) has been used widely to determine possible long-range correlations in data obtained from diverse settings. In a recent study [1], uncorrelated random spikes superimposed on the long-range correlated…
The particle-particle random phase approximation (ppRPA) within the hole-hole channel was recently proposed as an efficient tool for computing excitation energies of point defects in solids [J. Phys. Chem. Lett. 2024, 15, 2757-2764]. In…
The random-phase approximation to the ground state correlation energy (RPA) in combination with exact exchange (EX) has brought Kohn-Sham (KS) density functional theory one step closer towards a universal, "general purpose first principles…
We present novel algorithms for simulation optimization using random directions stochastic approximation (RDSA). These include first-order (gradient) as well as second-order (Newton) schemes. We incorporate both continuous-valued as well as…
Recent high resolution Compton scattering experiments clearly reveal that there are fundamental limitations to the conventional local density approximation (LDA) based description of the ground state electron momentum density (EMD) in…
We define a SDP framework based on the RLSTD algorithm and multivariate simplex B-splines. We introduce a local forget factor capable of preserving the continuity of the simplex splines. This local forget factor is integrated with the RLSTD…
Physics-informed machine learning and inverse modeling require the solution of ill-conditioned non-convex optimization problems. First-order methods, such as SGD and ADAM, and quasi-Newton methods, such as BFGS and L-BFGS, have been applied…
The random phase approximation (RPA) has emerged as a prominent first-principles method in material science, particularly to study the adsorption and chemisorption of small molecules on surfaces. However, its widespread application is…