Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Iterative method for evaluating the matrix representation of the generators in the unitary-group approach

A. Lev, M. Schlesinger, R. D. Kent

Published Dec 1, 1984• 3 citations
Publisher

Abstract

An iterative method is presented for the evaluation of the matrix representation of the group generators in the unitary-group approach to many-electron systems. The method yields, in addition, closed-form expressions and selection rules for nonvanishing matrix elements. Generator products (two-body operators) are treated by a scalar-product method.

DOI
10.1103/physreva.30.2859

Related papers

Two-body-operator matrix-element factorization technique in U(n)↓ SN unitary bases: Raising-raising operators

R. D. Kent, M. Schlesinger, Pardu S. Ponnapalli

A detailed exposition of explicit formulas used in the evaluation of raising-raising forms of two-body-operator matrix elements is presented. The methods are based on the use of the unitary-group distinct-row tabular-graphical representation of the many-particle basis. All matrix elements are expressible in the form of scalar and 2\ifmmode\times\else\texttimes\fi{}2 matrix factors. In order to facilitate the derivations of simple, computationally efficient forms for the matrix factors we develop a calculus based on elementary graphs. The methods are applicable to systems of particles involving spins greater than (1/2 and reduce to previously known results for the case of spin (1/2.

Physical Review A•Jan 1, 1989•15 citations

Two-body-operator matrix element factorization technique in U(n)↓ SN unitary bases. II. Raising-lowering operators

R. D. Kent, M. Schlesinger, Pardu S. Ponnapalli

A detailed exposition of explicit formulas used in the evaluation of raising-lowering forms of two-body-operator matrix elements is presented. The methods are based on the use of the unitary group distinct row table and graphical representation of the many-particle basis. All matrix elements are expressible in terms of scalar and simple matrix factors. In order to facilitate the derivations of simple, computationally efficient forms for the matrix factors, we utilize a recently developed calculus based on elementary graphs. The methods are applicable to systems of particles involving spins greater than (1/2 and reduce to previously known results for the case of spin (1/2.

Physical Review A•Apr 1, 1989•9 citations

Evaluation of two-body operator matrix elements in the unitary group approach

Hai‐Lun Lin, Yu-Fang Cao

The authors extend the Weyl graphical method to the two-body operator matrix elements in the many-particle system. The evaluation is accomplished by a simple and efficient recursion scheme.

Journal of Physics A Mathematical and General•Feb 21, 1990•0 citations

Matrix Elements of One- and Two-Body Operators in the Unitary Group Approach (I) — Formalism

Dai Lian-Rong, Feng Pan

The tensor algebraic method is used to derive general one- and two-body operator matrix elements within the representations, which are useful in the unitary group approach to the configuration interaction problems of quantum many-body systems.

Communications in Theoretical Physics•Feb 15, 2001•0 citations

Unitary-group approach (UGA) to the configuration interaction (CI) problems of the many-electron systems. II. Weyl graphical method of two-body operator matrix elements

Hai‐Lun Lin, Yu-Fang Cao

A recursive graphical approach for the evaluation of two-body operator matrix elements is presented. This new approach is simpler as well as clearer compared to other approaches.

The Journal of Chemical Physics•Sep 1, 1988•5 citations

Graphical Method of Evaluation of Matrix Elements in the Second Quantization Representation

Gintaras Merkelis

The graphical technique of evaluation in the second quantization representation of matrix elements of operators associated with the interactions in atoms is developed. The diagrams corresponding to operators and many-electron states given in terms of irreducible tensorial product of creation and annihilation operators are considered. The general rules for the construction of the diagrams for operators and matrix elements are presented. The procedures of reduction of the diagrams to obtain the algebraic expression are discussed.

Physica Scripta•Apr 1, 2001•10 citations
An iterative method is presented for the evaluation of the matrix representation of the group generators in the unitary-group approach to many-electron systems. The method yields, in addition, closed-form expressions and selection rules for nonvanishing matrix elements. Generator products (two-body operators) are treated by a scalar-product method.
A detailed exposition of explicit formulas used in the evaluation of raising-raising forms of two-body-operator matrix elements is presented. The methods are based on the use of the unitary-group distinct-row tabular-graphical representation of the many-particle basis. All matrix elements are expressible in the form of scalar and 2\ifmmode\times\else\texttimes\fi{}2 matrix factors. In order to facilitate the derivations of simple, computationally efficient forms for the matrix factors we develop a calculus based on elementary graphs. The methods are applicable to systems of particles involving spins greater than (1/2 and reduce to previously known results for the case of spin (1/2.
A detailed exposition of explicit formulas used in the evaluation of raising-lowering forms of two-body-operator matrix elements is presented. The methods are based on the use of the unitary group distinct row table and graphical representation of the many-particle basis. All matrix elements are expressible in terms of scalar and simple matrix factors. In order to facilitate the derivations of simple, computationally efficient forms for the matrix factors, we utilize a recently developed calculus based on elementary graphs. The methods are applicable to systems of particles involving spins greater than (1/2 and reduce to previously known results for the case of spin (1/2.
The graphical technique of evaluation in the second quantization representation of matrix elements of operators associated with the interactions in atoms is developed. The diagrams corresponding to operators and many-electron states given in terms of irreducible tensorial product of creation and annihilation operators are considered. The general rules for the construction of the diagrams for operators and matrix elements are presented. The procedures of reduction of the diagrams to obtain the algebraic expression are discussed.