Program for calculating SU(4) Clebsch–Gordan coefficients

The SU(4) Clebsch–Gordan coefficients of the decomposition {Na}⊗{Nb}→{N}{Na}⊗{Nb}→{N} are calculated for arbitrary irreducible representations {Na}{Na}, {Nb}{Nb} and {N}{N}. They are efficiently computed for the group chain SU(4) ⊃ SU(3)×U(1) ⊃ SU(2)×U(1) ⊃ U(1) using the eigenfunction method along with recurrence relations.Program summaryProgram title: CGSU4Catalogue identifier: AEBL_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEBL_v1_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 2847No. of bytes in distributed program, including test data, etc.: 23 794Distribution format: tar.gzProgramming language: Fortran 95Computer: Personal computerOperating system: Linux, WindowsRAM: 2 MBClassification: 4.2Subprograms used: ACRM_v1_0; Title: SU(3) [1]Nature of problem: The SU(4) Clebsch–Gordan coefficients according to the group chain SU(4) ⊃ SU(3) × U(1) ⊃ SU(2) × U(1) ⊃ U(1) are calculated for arbitrary couplings.Solution method: The eigenfunctions method in combination with recurrence relations is used to generate tables of the SU(4) ⊃ SU(3) × U(1) isoscalar factors for the decomposition {Na}⊗{Nb}→{N}γ{Na}⊗{Nb}→{N}γ with the multiplicity label γ. The SU(4) Clebsch–Gordan coefficients are then composed by these isoscalar factors and SU(3) Clebsch–Gordan coefficients according to the Racah factorization lemma.Restrictions: The dimensions of the involved representations are limited by the size of the arrays defined in the program.Additional comments:   If many Clebsch–Gordan coefficients are needed for the same decomposition {Na}⊗{Nb}→{N}γ{Na}⊗{Nb}→{N}γ, the running time is significantly reduced if the table of isoscalar factors is calculated only once. The SU(3) code [1] and the code for eigen, a matrix diagonalization program (IBM scientific subroutine package) are included in the CGSU4 code package.Running time: The running time sensitively depends on the specific Clebsch–Gordan decomposition and the dimensions of the involved representations, varying from parts of a second to a minute.References:[1] Y. Akiyama, J.P. Draayer, Comput. Phys. Comm. 5 (1973) 405.