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Manuscript Title: Data structure techniques for the graphical special unitary group approach to arbitrary spin representations.
Authors: R.D. Kent, M. Schlesinger
Program title: GENDRT, DRTDIM
Catalogue identifier: AATF_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 43(1987)413
Programming language: Pascal.
Computer: IBM PC, PC/XT, PC/AT.
Operating system: MS-DOS (PC-DOS) VERSION 2.1 OR HIGHER.
RAM: 128K words
Word size: 16
Peripherals: disc.
Keywords: General purpose, Algebras, Su(n) groups, Theory graph, Structure graphical data, Arbitrary spin Representations, Spectroscopy, Micro-computer Applications.
Classification: 4.2.

Nature of problem:
For the purpose of computing matrix elements of quantum mechanical operators in complex N-particle systems it is necessary that as much of each irreducible representation be stored in high-speed memory as possible inorder to achieve the highest possible rate of computations. A graph theoretic approach to the representation of N-particle systems involving arbitrary single-particle spin is presented. The method involves a generalization of a technique employed by Shavitt in developing the graphical unitary group approach (GUGA) to electronic spin-orbitals. The methods implemented in GENDRT and DRTDIM overcome many deficiencies inherent in other approaches, particularly with respect to utilization of memory resources, computational efficiency in the recognition and evaluation of non-zero matrix elements of certain group theoretic operators and complete labelling of all the basis states of the permutation symmetry (SN) adapted irreducible representations of SU(N) groups.

Solution method:
The group theoretic labels provided by the symmetric group partitioning of the special unitary group are utilized directly to construct a two- rooted, multiply connected graphical data structure. The construction of the graph is performed using recursive techniques which allow, alternatively, the simple enumeration of the basis states (DRTDIM) or the computation and dynamic allocation of the full graph structure (GENDRT).

Depending on input parameters the complexity of cases is restricted by memory and real time considerations which vary for GENDRT and DRTDIM respectively.

Running time:
Typical cases of moderate complexity require from minutes to hours, depending on the inputted parameters used to define each irrep.