Efficient algorithm for representations of U(3) in U(N)

• Published in: Computer physics communications Vol. 244; pp. 442 - 447
• Main Authors: Langr, Daniel, Dytrych, Tomáš, Draayer, Jerry P., Launey, Kristina D., Tvrdík, Pavel
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01-11-2019
• Subjects: C++; Group representation; Nuclear structure; OpenMP; Three-dimensional harmonic oscillator; U symmetry; Three-dimensional harmonic oscillator; Nuclear structure; C++; Group representation; OpenMP; U symmetry
• ISSN: 0010-4655; 1879-2944
• DOI: 10.1016/j.cpc.2019.05.018

An efficient algorithm for enumerating representations of U(3) that occur in a representation of the unitary group U(N) is introduced. The algorithm is applicable to U(N) representations associated with a system of identical fermions (protons, neutrons, electrons, etc.) distributed among the N=(η+1)(η+2)∕2 degenerate eigenstates of the ηth level of the three-dimensional harmonic oscillator. A C++ implementation of the algorithm is provided and its performance is evaluated. The implementation can employ OpenMP threading for use in parallel applications.
Program Title:UNtoU3.h
Program files doi:http://dx.doi.org/10.17632/3g4w8f9vdk.1
Licensing provisions: MIT
Programming language: C++
Nature of problem: The determination of the complete set of U(3) irreducible representations (irreps) that occurs in a representation of U(N), where N=(η+1)(η+2)∕2 is the degeneracy of the ηth harmonic oscillator shell.
Solution method: The resulting set of U(3) irreps is determined by applying a simple difference relation to the U(3) weight distribution of the Gelfand basis states spanning a given U(N) irrep.