Description Of Correlation Effects Research Articles

Mapping renormalized coupled cluster methods to quantum computers through a compact unitary representation of nonunitary operators

Nonunitary theories are commonly seen in the classical simulations of quantum systems. Among these theories, the method of moments of coupled cluster equations (MMCCs) and the ensuing classes of the renormalized coupled cluster (CC) approaches have evolved into one of the most accurate approaches to describe correlation effects in various quantum systems. The MMCC formalism provides an effective way for correcting the energies of approximate CC formulations (parent theories) using moments, or CC equations, that are not used to determine approximate cluster amplitudes. In this paper, we propose a quantum algorithm for computing MMCC ground-state energies that provides two main advantages over classical computing or other quantum algorithms: (i) the possibility of forming superpositions of CC moments of arbitrary ranks in the entire Hilbert space and using an arbitrary form of the parent cluster operator for MMCC expansion, and (ii) significant reduction in the number of measurements in quantum simulation through a compact unitary representation for a generally nonunitary operator. We illustrate the robustness of our approach over a broad class of test cases, including $\ensuremath{\sim}40$ molecular systems with varying basis sets encoded using 4--40 qubits, and we exhibit the detailed MMCC analysis for the 8-qubit half-filled, four-site, single impurity Anderson model and the 12-qubit hydrogen fluoride molecular system from the corresponding noise-free and noisy MMCC quantum computations. We also outline the extension of the MMCC formalism to the case of a unitary CC wave-function Ansatz.

Single-boson exchange functional renormalization group application to the two-dimensional Hubbard model at weak coupling

We illustrate the algorithmic advantages of the recently introduced single-boson exchange (SBE) formulation for the one-loop functional renormalization group (fRG), by applying it to the two-dimensional Hubbard model on a square lattice. We present a detailed analysis of the fermion-boson Yukawa couplings and of the corresponding physical susceptibilities by studying their evolution with temperature and interaction strength, both at half filling and finite doping. The comparison with the conventional fermionic fRG decomposition shows that the rest functions of the SBE algorithm, which describe correlation effects beyond the SBE processes, play a negligible role in the weak-coupling regime above the pseudo-critical temperature, in contrast to the rest functions of the conventional fRG. Remarkably, they remain finite also at the pseudo-critical transition, whereas the corresponding rest functions of the conventional fRG implementation diverge. As a result, the SBE formulation of the fRG flow allows for a substantial reduction of the numerical effort in the treatment of the two-particle vertex function, paving a promising route for future multiboson and multiloop extensions.Graphic abstract

Relativistic reduced density matrix functional theory

As a new approach to efficiently describe correlation effects in the relativistic quantum world we propose to consider reduced density matrix functional theory, where the key quantity is the first-order reduced density matrix (1-RDM). In this work, we first introduce the theoretical foundations to extend the applicability of this theory to the relativistic domain. Then, using the so-called no-pair (np) approximation, we arrive at an approximate treatment of the relativistic effects by focusing on electronic wavefunctions and neglecting explicit contributions from positrons. Within the np approximation the theory becomes similar to the nonrelativistic case, with as unknown only the functional that describes the electron-electron interactions in terms of the 1-RDM. This requires the construction of functional approximations, and we therefore also present the relativistic versions of some common RDMFT approximations that are used in the nonrelativistic context and discuss their properties.

Possibilities of the Molecular Modeling of Kinetic Processes under Supercritical Conditions

Current possibilities of modeling the kinetics of supercritical processes are considered, based on the theory of an absolute rate of the reaction for non-ideal reaction systems, which considers intermolecular interactions that change the effective energy of activation of elementary stages. This allows the theory to describe the rates of elementary stages for arbitrary temperatures and densities of the reagent in different phases. Application of this theory in a wide range of state parameters (pressure and temperature) is examined while calculating elementary bimolecular reactions and dissipative coefficients under supercritical conditions. Generalized dependences within the law of corresponding states are calculated for the compressibility, viscosity, and thermal conductivity coefficients of pure substances and those of the compressibility, self- and mutual diffusion, and viscosity of binary mixtures. The effect density and temperature have on the rates of elementary stages under supercritical conditions is demonstrated for a reaction’s effective energies of activation, diffusion and share coefficients, and equilibrium constants of adsorption. Differences between models with effective parameters and the prospects for developing them by allowing for differences in size and contributions from the vibrational motions of components are described, along with ways of improving the accuracy of describing correlation effects.

The influence of defects on magnetic properties of fcc-Pu

The influence of vacancies and interstitial atoms on magnetism in Pu is considered in the framework of the density functional theory. The crystal structure relaxation arising due to various types of defects is calculated using the molecular dynamics method with a modified embedded atom model. The local density approximation with explicit inclusion of Coulomb and spin-orbit interactions is applied in matrix invariant form to describe correlation effects in Pu with these types of defects. The calculations show that both vacancies and interstitials give rise to local moments in the f-shell of Pu in good agreement with experimental data for aged Pu. Magnetism appears due to the destruction of a delicate balance between spin-orbit and exchange interactions.

Field effect on surface states in a doped Mott-insulator thin film

Surface effects of a doped thin film made of a strongly correlated material are investigated both in the absence and presence of a perpendicular electric field. We use an inhomogeneous Gutzwiller approximation for a single band Hubbard model in order to describe correlation effects. For low doping, the bulk value of the quasiparticle weight is recovered exponentially deep into the slab, but with increasing doping, additional Friedel oscillations appear near the surface. We show that the inverse correlation length has a power-law dependence on the doping level. In the presence of an electrical field, considerable changes in the quasiparticle weight can be realized throughout the system. We observe a large difference (as large as five orders of magnitude) in the quasiparticle weight near the opposite sides of the slab. This effect can be significant in switching devices that use the surface states for transport.

Mathematical explanation of the predictive power of the X-level approach reaction noise estimator method

The X-level Approach Reaction Noise Estimator (XARNES) method has been developed previously to study reaction noise in well mixed reaction volumes. The method is a typical moment closure method and it works by closing the infinite hierarchy of equations that describe moments of the particle number distribution function. This is done by using correlation forms which describe correlation effects in a strict mathematical way. The variable X is used to specify which correlation effects (forms) are included in the description. Previously, it was argued, in a rather informal way, that the method should work well in situations where the particle number distribution function is Poisson-like. Numerical tests confirmed this. It was shown that the predictive power of the method increases, i.e. the agreement between the theory and simulations improves, if X is increased. In here, these features of the method are explained by using rigorous mathematical reasoning. Three derivative matching theoremsare proven which show that the observed numerical behavior is generic to the method.

Computational pair density functional theory: A proposal for the kinetic energy functional

We present a computational pair density (PD) functional theory using multiple Slater determinants in constructing the PD. Compared to the effective initial scheme [M. Higuchi and K. Higuchi, Phys. Rev. B 78, 125101 (2008)], the search region for the ground-state PD is substantially extended within the set of $N$-representable PDs. The merit of the present scheme is to guarantee the resultant PD to be $N$-representable and to describe correlation effects beyond the effective initial scheme, which enables us to tackle with the development of the approximate form of the kinetic energy functional. We derive two restrictive conditions on the kinetic energy functional. With the aid of these restrictive conditions, we also propose several types of approximate functionals of the kinetic energy. To check the abilities and limitations of the present scheme including such approximate functionals, actual calculations are performed for the neutral neon atom. The results show that the present scheme provides the $N$-representable and correlated PDs, though it would have some limitations. What we need to do first for improvement of the computational PD functional theory is that the development of the approximate functional of the kinetic energy is further advanced along the present scheme.

Ab initio study of Hg-Hg and E112-E112 van der Waals interactions

The ground electronic state of the eka-mercury dimer (E1122) was studied within the model of generalized relativistic effective core potentials. A combined procedure based on describing correlation effects by the scalar relativistic coupled-cluster method and on taking into account spin-dependent interactions by means of density-functional theory was used in the calculations. A high accuracy of this approach was confirmed by the results of similar calculations for the mercury dimer. It was found that the bond length is nearly 0.4 A shorter in E1122 than in Hg2 and that the dissociation energy of the former is approximately twice as high as that of the latter dimer.

Effective quadrupole-quadrupole interaction from density functional theory

The density functional theory of nuclear structure provides a many-particle wave function that is useful for static properties, but an extension of the theory is necessary to describe correlation effects or other dynamic properties. Here we propose a procedure to extend the theory by mapping the properties of the self-consistent mean-field Hamiltonian onto an effective shell-model Hamiltonian with two-body interactions. In this initial study, we consider the sd-shell nuclei Ne-20, Mg-24, Si-28, and Ar-36. Our first application is in the framework of the USD shell-model Hamiltonian, using its mean-field approximation to construct an effective Hamiltonian and partially recover correlation effects. We find that more than half of the correlation energy is due to the quadrupole interaction. We then follow a similar procedure but using the SLy4 Skyrme energy functional as our starting point and truncating the space to the spherical $sd$ shell. The constructed shell-model Hamiltonian is found to satisfy minimal consistency requirements to reproduce the properties of the mean-field solution. The quadrupolar correlation energies computed with the mapped Hamiltonian are reasonable compared with those computed by other methods.

Correlation and spin polarization in quantum dots: Local spin density functional theory revisited

AbstractUsing quantum dot artificial atoms as a simple toy model, we reflect on the question of whether spin density functional theory (SDFT) can accurately describe correlation effects in low‐dimensional fermion systems. Different expressions for the local density approximation of the exchange‐correlation energy for the two‐dimensional electron gas, such as the much‐used functional of Tanatar and Ceperley, and the recent suggestion by Attaccalite et al., are compared with the results of a numerical diagonalization of the many‐body Hamiltonian matrix in the limit of small electron numbers. For systems with degeneracies, as shown in the present work for the example of a spin triplet with S = 1, the direct comparison with configuration interaction (CI) methods demonstrates that the spin representation of SDFT may, under certain circumstances, produce artificial energy splittings between states that belong to the same spin multiplet. For a singlet ground state with S = Sz = 0, however, the correlation functions of the CI solutions confirm the spin‐density wave states found earlier within the SDFT method. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005

Effective procedure for energy optimizing antisymmetrized geminal power states

A procedure for energy optimizing an antisymmetrized geminal power state, which contains a description of correlation effects in an unbiased fashion, is presented. This procedure overcomes difficulties and shortcomings of past optimization procedures for antisymmetrized geminal power states. It is shown that the computational cost scales as r5, where r is the size of the spin orbital atomic basis set, which is superior to the scaling costs of multiexcited complete active space self-consistent field calculations, but unlike such calculations their is no preselection of configurations or excitation level. The variational parameters are the geminal coefficients with respect to a fixed atomic orbital basis, which allows one to classify these variables into chemically significant and non significant ones according to their magnitudes and thus reduce size of calculations.

Treatment of correlation effects in electron momentum density: density functional theory and beyond

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 solids. In order to go beyond the framework of the density function theory (DFT), we consider for the correlated system a BCS-like approach in which we start with a singlet pair wavefunction or a ‘geminal’ from which the many body wavefunction is then constructed by taking an antisymmetrized geminal product (AGP). A relatively simple practical implementation of the AGP method is developed where the one-particle orbitals are approximated by the Kohn–Sham solutions used in standard band computations, and the orbital-dependent BCS energy scale Δ i is determined through a readily computed exchange-type integral. The methodology is illustrated by considering EMD and Compton profiles in Li, Be and Al. It is found that in Li the present scheme predicts a substantial renormalization of the LDA result for the EMD; in Be, the computed correlation effect is anisotropic, while in Al, the deviations from the LDA are relatively small. These theoretical predictions are in qualitative accord with the corresponding experimental observations on Li, Be and Al, and indicate the potential of the AGP method for describing correlation effects on the EMD in wide classes of materials.

Coupled rearrangement channel calculation of the fine and hyperfine structures of the antiprotonic helium atom

We precisely calculate the fine and hyperfine structure splittings of the $(v,J)=(1,35)$ state in the antiprotonic helium atom, where $v$ is the vibrational quantum number and $J$ is the total orbital angular momentum. The coupled rearrangement channel method is employed to efficiently describe correlation effects in the three-body system with atomic and molecular characters. An accuracy of better than ${\ensuremath{\alpha}}^{2}\ensuremath{\approx}50\mathrm{ppm}$ has been achieved. The result obtained is in good agreement with the previous calculation within $\ensuremath{\sim}200 \mathrm{ppm}.$ We also examine the correlation effects, in particular orbital polarization effects.

Two-color photoionization of helium above theN=2ionization threshold

We study two-color photoionization of helium in the region of the 3s3d D-1 autoionizing state with resonant excitation of the intermediate 2s2p P-1 autoionizing state. We show that the corresponding time-dependent Schrodinger equation may be solved by expanding the total wave function on a few complex energy states. Perimetric coordinates are used to describe correlation effects accurately. Populations at the end of the interaction as well as photoionization probabilities are studied as a function of the laser pulse duration acid both frequencies. Our calculations show that many continua play a crucial role at high intensities. [S1050-2947(99)06308-8].

Ground-state energies of isoelectronic atomic series from density-functional theory: Exploring the accuracy of density functionals

The performance of commonly used correlation and exchange-correlation functionals has been studied for highly charged atomic ions. Calculated energies have been compared with exact nonrelativistic energies of atomic species with 2--18 electrons for nuclei from $Z=2$ (He) to $Z=26$ (Ni). It is found that all density functionals considered here reveal problems in the description of correlation effects as a function of nuclear charge Z.

Correlation effects in the quasi-one-dimensional charged Bose condensate

We describe correlation effects in the charged quasi-one-dimensional Bose condensate with parabolic confinement. Many-body effects are calculated with the sum-rule version of the Singwi, Tosi, Land, and Sj\"olander theory. We give numerical and analytical results for the local-field correction, the pair-distribution function, the correlation energy, and the compressibility of the Bose condensate. The results are given as a function of the Wigner-Seitz parameter ${r}_{s}$ and the wire-width parameter $b.$ The exact long-wavelength behavior of the plasmon dispersion is investigated using the compressibility sum rule.

Correlation Effects in Small-Angle Neutron Scattering from Closely Packed Spheres

Computer simulations are used to investigate the effects of interparticle correlations on small-angle neutron scattering spectra of systems of closely packed solid spheres. By the use of computer-generated systems containing large numbers of different sized spheres, the SANS spectra are calculated by exact summation of the form factors. The accuracy of the calculation is limited only by the maximum size of the system that can reasonably be run on the computer. The results from these simulations are compared with theoretical predictions and a simple generalization of the formula for monodisperse systems is tested. It is shown that, for a wide range of particle size distributions, this simple formula is sufficient to describe correlation effects in polydisperse systems.

Memory effects and virial corrections in nonequilibrium dense systems.

A dense interacting Bose or Fermi gas is considered. Within the Kadanoff-Baym real-time Green-function technique a generalized kinetic equation is derived in the nonequilibrium ladder approximation. As a Markovian limit the Boltzmann-Uehling-Uhlenbeck equation is recovered. The relevance of retardation effects in the kinetic equation of dense systems is shown. It turns out that the stationary solution of the generalized kinetic equation reproduces the second virial coefficient of the equation of state, including the Beth-Uhlenbeck quantum corrections. We establish a generalized kinetic equation describing correlation effects in a consistent approach to nonequilibrium for Bose and Fermi systems. In this way we give a generalization of the Beth-Uhlenbeck formula that applies to nonequilibrium and to finite systems. The derivation makes use of the time dependent T-matrix equation, which establishes a generalization of the Bethe-Goldstone equation. The correlated parts of the density and energy, which can be interpreted as virial corrections, are thermodynamically consistent. In this way global energy conservation is fulfilled.

Considerations on correlation effects in π-electron systems

Conventional models use antisymmetrized configurations of molecular orbitals (MOs) expressed as linear combinations of atomic orbitals (LCAOs) to describe correlation effects. In the free electron (FE) model and beyond the antisymmetry condition is neglected. This leads to a strong simplification and to physical transparency in describing correlation effects by electron repulsion without losing the essence, determining spectroscopic properties. Examples are studied where the correlation effects in the ground state and in the excited state are not very different (strong absorption band in dyes and polyenes) and examples where this is not the case (first absorption band in porphyrin, which is diminished in intensity to a tenth by electron correlation, transition into the 2 1Ag state in polyenes, which is shifted below the 1 1Bu state by electron correlation). The appropriate evaluation of the electron repulsion integral is crucial in quantitative approaches. The evaluation procedures in the FE approach and in conventional models are critically considered. The nearly free electron (NFE) model approach (numerical solution of 1D Schrödinger equations for appropriate model potentials and straightforward numerical evaluation of interaction integrals) avoids difficulties in using and overstressing perturbation theory.