Related papers: Reproduction of exact solutions of Lipkin model by…
We investigate the applicability of finite temperature random phase approximation (RPA) using a solvable Lipkin model. We show that the finite temperature RPA reproduces reasonably well the temperature dependence of total strength, both for…
A self-consistent random phase approximation (RPA) is proposed as an effective Hamiltonian method in Light-Front Field Theory (LFFT). We apply the general idea to the light-front massive Schwinger model to obtain a new bound state equation…
Concerning the su(2)-Lipkin model, the calculation of the excitation energy to the 1st excited-state gives rise to the following fact: The two results based on the exact treatment and the conventional random phase approximation (RPA) are in…
We show that it is possible to restore the symmetry associated with the Goldstone mode within the Self Consistent Random Phase Approximation (SCRPA) applied to the three-level Lipkin model. We determine one and two-body densities as very…
We propose a practical method to solve the random-phase approximation (RPA) in the self-consistent Hartree-Fock (HF) and density-functional theory. The method is based on numerical evaluation of the residual interactions utilizing finite…
Particle-number projection within the Lipkin-Nogami (LN) method is applied to the self-consistent quasiparticle random-phase approximation (SCQRPA), which is tested in an exactly solvable multi-level pairing model. The SCQRPA equations are…
The accurate computation of non-linear optical properties (NLOPs) in large polymers requires accounting for electronic correlation effects with a reasonable computational cost. The Random Phase Approximation (RPA) used in the adiabatic…
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 a real-space method for computing the random phase approximation (RPA) correlation energy within Kohn-Sham density functional theory, leveraging the low-rank nature of the frequency-dependent density response operator. In…
Random Phase Approximation (RPA) is the theory most commonly used to describe the excitations of many-body systems. In this article, the secular equations of the theory are obtained by using three different approaches: the equation of…
Coupled cluster theory provides hierarchical many-particle models and is presently considered as the ultimate benchmark in quantum chemistry. Despite is practical significance, a rigorous mathematical analysis of its properties is still in…
The optimized effective potential (OEP) method presents an unambiguous way to construct the Kohn-Sham potential corresponding to a given diagrammatic approximation for the exchange-correlation functional. The OEP from the random-phase…
We compute the energy functional of a three-level Lipkin model via a Legrendre transform and compare exact numerical results with analytical solutions obtained from the random phase approximation (RPA). Except for the region of the phase…
Over time, many different theories and approaches have been developed to tackle the many-body problem in quantum chemistry, condensed-matter physics, and nuclear physics. Here we use the helium atom, a real system rather than a model, and…
The Lipkin-Meshkov-Glick model is used to examine the validity of some approximate methods in a many-body theory at finite temperatures. Namely, the thermal random phase approximation (TRPA) and the thermal renormalized random phase…
Properties of solutions of the RPA equation is reanalyzed mathematically, which is defined as a generalized eigenvalue problem of the stability matrix $\mathsf{S}$ with the norm matrix $\mathsf{N}=\mathrm{diag.}(1,-1)$. As well as physical…
A limitation common to all extensions of random-phase approximation including only particle-hole configurations is that they violate to some extent the energy weighted sum rules. Considering one such extension, the improved RPA (IRPA),…
We present an efficient implementation of the random phase approximation (RPA) for molecular systems within the domain-based local pair natural orbital (DLPNO) framework. With optimized parameters, DLPNO-RPA achieves approximately 99.9%…
The random phase approximation (RPA) for the correlation energy functional of density functional theory has recently attracted renewed interest. Formulated in terms of the Kohn-Sham (KS) orbitals and eigenvalues, it promises to resolve some…
The particle-particle random phase approximation (pp-RPA) has been shown to be capable of describing double, Rydberg, and charge transfer excitations, for which the conventional time-dependent density functional theory (TDDFT) might not be…