Program for calculating SU(4) Clebsch–Gordan coefficients

Abstract

The SU(4) Clebsch–Gordan coefficients of the decomposition { N a } ⊗ { N b } → { N } are calculated for arbitrary irreducible representations { N a } , { N b } and { 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 summary Program title: CGSU4 Catalogue identifier: AEBL_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEBL_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 2847 No. of bytes in distributed program, including test data, etc.: 23 794 Distribution format: tar.gz Programming language: Fortran 95 Computer: Personal computer Operating system: Linux, Windows RAM: 2 MB Classification: 4.2 Subprograms 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 { N a } ⊗ { N b } → { 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 { N a } ⊗ { N b } → { 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.