Longitudinal static optical properties of hydrogen chains: finite field extrapolations of matrix product state calculations

We have implemented the sweep algorithm for the variational optimization of SU(2) x U(1) (spin and particle number) invariant matrix product states (MPS) for general spin and particle number invariant fermionic Hamiltonians. This class includes non-relativistic quantum chemical systems within the Born-Oppenheimer approximation. High-accuracy ab-initio finite field results of the longitudinal static polarizabilities and second hyperpolarizabilities of one-dimensional hydrogen chains are presented. This allows to assess the performance of other quantum chemical methods. For small basis sets, MPS calculations in the saturation regime of the optical response properties can be performed. These results are extrapolated to the thermodynamic limit.Comment: Submitted to J. Chem. Phy

A primal-dual semidefinite programming algorithm tailored to the variational determination of the two-body density matrix

The quantum many-body problem can be rephrased as a variational determination of the two-body reduced density matrix, subject to a set of N-representability constraints. The mathematical problem has the form of a semidefinite program. We adapt a standard primal-dual interior point algorithm in order to exploit the specific structure of the physical problem. In particular the matrix-vector product can be calculated very efficiently. We have applied the proposed algorithm to a pairing-type Hamiltonian and studied the computational aspects of the method. The standard N-representability conditions perform very well for this problem.Comment: 24 pages, 5 figures, submitted to the Journal of Computational Physic

Solving the Richardson equations for Fermions

Forty years ago Richardson showed that the eigenstates of the pairing Hamiltonian with constant interaction strength can be calculated by solving a set of non-linear coupled equations. However, in the case of Fermions these equations lead to singularities which made them very hard to solve. This letter explains how these singularities can be avoided through a change of variables making the Fermionic pairing problem numerically solvable for arbitrary single particle energies and degeneracies.Comment: 5 pages, 4 figures, submitted to Phys.Rev.

Correlation effects in single-particle overlap functions and one-nucleon removal reactions

Single-particle overlap functions and spectroscopic factors are calculated on the basis of the one-body density matrices (ODM) obtained for the nucleus $^{16}O$ employing different approaches to account for the effects of correlations. The calculations use the relationship between the overlap functions related to bound states of the (A-1)-particle system and the ODM for the ground state of the A-particle system. The resulting bound-state overlap functions are compared and tested in the description of the experimental data from (p,d) reactions for which the shape of the overlap function is important.Comment: 11 pages, 4 figures include

Variational determination of the second-order density matrix for the isoelectronic series of beryllium, neon and silicon

The isoelectronic series of Be, Ne and Si are investigated using a variational determination of the second-order density matrix. A semidefinite program was developed that exploits all rotational and spin symmetries in the atomic system. We find that the method is capable of describing the strong static electron correlations due to the incipient degeneracy in the hydrogenic spectrum for increasing central charge. Apart from the ground-state energy various other properties are extracted from the variationally determined second-order density matrix. The ionization energy is constructed using the extended Koopmans' theorem. The natural occupations are also studied, as well as the correlated Hartree-Fock-like single particle energies. The exploitation of symmetry allows to study the basis set dependence and results are presented for correlation-consistent polarized valence double, triple and quadruple zeta basis sets.Comment: 19 pages, 7 figures, 3 tables v2: corrected typo in Eq. (52

Quasiparticle properties in a density functional framework

We propose a framework to construct the ground-state energy and density matrix of an N-electron system by solving selfconsistently a set of single-particle equations. The method can be viewed as a non-trivial extension of the Kohn-Sham scheme (which is embedded as a special case). It is based on separating the Green's function into a quasi-particle part and a background part, and expressing only the background part as a functional of the density matrix. The calculated single-particle energies and wave functions have a clear physical interpretation as quasiparticle energies and orbitals.Comment: 12 pages, 1 figure, to be published in Phys. Rev.

Quasiparticles in Neon using the Faddeev Random Phase Approximation

The spectral function of the closed-shell Neon atom is computed by expanding the electron self-energy through a set of Faddeev equations. This method describes the coupling of single-particle degrees of freedom with correlated two-electron, two-hole, and electron-hole pairs. The excitation spectra are obtained using the Random Phase Approximation, rather than the Tamm-Dancoff framework employed in the third-order algebraic diagrammatic contruction [ADC(3)] method. The difference between these two approaches is studied, as well as the interplay between ladder and ring diagrams in the self-energy. Satisfactory results are obtained for the ionization energies as well as the energy of the ground state with the Faddeev-RPA scheme that is also appropriate for the high-density electron gas.Comment: Revised manuscript. The working equations of the Faddeev-RPA method are included in the Appendi

Correlations in Nuclei: Self-Consistent Treatment and the BAGEL Approach

An approach is presented which allows a self-consistent description of the fragmentation of single-particle strength for nucleons in finite nuclei employing the Greens function formalism. The self-energy to be considered in the Dyson equation for the single-particle Greens function contains all terms of first (Hartree-Fock) and second order in the residual interaction. It is demonstrated that the fragmentation of the single-particle strength originating from the terms of second order can efficiently be described in terms of the so-called BAGEL approximation. Employing this approximation the self-energy can be evaluated in a self-consistent way, i.e. the correlations contained in the Greens function are taken into account for the evaluation of the self-energy. As an example this scheme is applied to the nucleus $^{16}O$, using a realistic nucleon nucleon interaction. The effects of the correlations on the occupation probabilities and the binding energy are evaluated.Comment: 9 page

Polynomial scaling approximations and dynamic correlation corrections to doubly occupied configuration interaction wave functions

A class of polynomial scaling methods that approximate Doubly Occupied Configuration Interaction (DOCI) wave functions and improve the description of dynamic correlation is introduced. The accuracy of the resulting wave functions is analysed by comparing energies and studying the overlap between the newly developed methods and full configuration interaction wave functions, showing that a low energy does not necessarily entail a good approximation of the exact wave function. Due to the dependence of DOCI wave functions on the single-particle basis chosen, several orbital optimisation algorithms are introduced. An energy-based algorithm using the simulated annealing method is used as a benchmark. As a computationally more affordable alternative, a seniority number minimising algorithm is developed and compared to the energy based one revealing that the seniority minimising orbital set performs well. Given a well-chosen orbital basis, it is shown that the newly developed DOCI based wave functions are especially suitable for the computationally efficient description of static correlation and to lesser extent dynamic correlation.Fil: Van Raemdonck, Mario. Ghent University; BélgicaFil: Alcoba, Diego Ricardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; ArgentinaFil: Poelmans, Ward. Ghent University; BélgicaFil: De Baerdemacker, Stijn. Ghent University; BélgicaFil: Torre, Alicia. Universidad del País Vasco; EspañaFil: Lain, Luis. Universidad del País Vasco; EspañaFil: Massaccesi, Gustavo Ernesto. Universidad de Barcelona. Facultad de Física. Departamento de Física Fomental; EspañaFil: Van Neck, D.. Ghent University; BélgicaFil: Bultinck, P.. Ghent University; Bélgic