Related papers: Generalized nonorthogonal matrix elements for arbi…
Matrix elements between nonorthogonal Slater determinants represent an essential component of many emerging electronic structure methods. However, evaluating nonorthogonal matrix elements is conceptually and computationally harder then…
A review of methods for finding general expressions for matrix elements (non-diagonal with respect to configurations included) of any one- and two-particle operator for an arbitrary number of shells in an atomic configuration is given.…
In this communication, we examine new formalisms for the construction of the external space when correlating reference wavefunctions built from nonorthogonal determinant expansions. Defining the external space in nonorthogonal approaches is…
A general method is described for finding algebraic expressions for matrix elements of any one- and two-particle operator for an arbitrary number of subshells in an atomic configuration, requiring neither coefficients of fractional…
The Goldstone-Brueckner perturbation theory is extended to incorporate in a simple way correlations associated with large amplitude collective motions in nuclei. The new energy expansion making use of non-orthogonal vacua still allows to…
We present an extension of the L\"owdin strategy to find arbitrary matrix elements of generic Slater determinants. The new method applies to arbitrary number of fermionic operators, even in the case of a singular overlap matrix.
Precision tests of the Standard Model and searches for beyond the Standard Model physics often require nuclear structure input. There has been a tremendous progress in the development of nuclear ab initio techniques capable of providing…
Ab initio studies of atomic nuclei are based on Hamiltonians including one-, two- and three-body operators with very complicated structures. Traditionally, matrix elements of such operators are expanded on a Harmonic Oscillator…
We use ab initio electronic-structure methods to investigate random-matrix theory (RMT) universality in molecular electronic structure. Using single-reference electronic structure methods, including Hartree-Fock, configuration-interaction…
Multi-reference calculations along the lines of the Generator Coordinate Method or the restoration of broken symmetries within the nuclear Energy Density Functional (EDF) framework are becoming a standard tool in nuclear structure physics.…
We tabulate angularly reduced fourth-order many-body corrections to matrix elements for univalent atoms, derived in [A. Derevianko and E.D. Emmons, Phys. Rev. A 65, 052115 (2002)]. In particular we focused on practically important diagrams…
Fourth-order many-body corrections to matrix elements for atoms with one valence electron are derived. The obtained diagrams are classified using coupled-cluster-inspired separation into contributions from n-particle excitations from the…
Many models for chaotic systems consist of joining two integrable systems with incompatible constants of motion. The quantum counterparts of such models have a propagator which factorizes into two integrable parts. Each part can be…
We present an efficient numerical method for computing Hamiltonian matrix elements between non-orthogonal Slater determinants, focusing on the most time-consuming component of the calculation that involves a sparse array. In the usual case…
A generalized covariant method of analysis applicable to frames for which time is not orthogonal to space, such as spacetime around a star possessing angular momentum or on a rotating disk, is presented. Important aspects of such an…
Density matrix perturbation theory [Phys. Rev. Lett. Vol. 92, 193001 (2004)] provides an efficient framework for the linear scaling computation of response properties [Phys. Rev. Lett. Vol. 92, 193002 (2004)]. In this article, we generalize…
We derive a formalism, the separation method, for the efficient and accurate calculation of two-body matrix elements for a Gaussian potential in the cylindrical harmonic-oscillator basis. This formalism is of critical importance for…
Motivated by a model in quantum computation we study orthogonal sets of integral vectors of the same norm that can be extended with new vectors keeping the norm and the orthogonality. Our approach involves some arithmetic properties of the…
In this paper, we examine the structure of systems that are weighted homogeneous for several systems of weights, and how it impacts the computation of Gr\"obner bases. We present several linear algebra algorithms for computing Gr\"obner…
A recursive calculational scheme is developed for matrix elements in the generalized seniority scheme for the nuclear shell model. Recurrence relations are derived which permit straightforward and efficient computation of matrix elements of…