SU(N) Clebsch-Gordan coefficients and non-Abelian symmetries

The numerical treatment of models with SU($N$) benefits greatly from the Wigner-Eckart theorem. Its application requires the explicit knowledge of the Clebsch-Gordan coefficients (CGCs) of the group SU($N$). We present an algorithm for the explicit numerical calculation of SU($N$) CGCs based on the \emph{Gelfand-Tsetlin pattern} calculus. Further exploitation of the Weyl symmetry of SU($N$) irreducible representations (irreps) leads to a significant speed-up compared to our previous algorithm (J.~Math.~Phys.\ 52, 023507, 2011). Our algorithm works for arbitrary $N$ and tensor products of two arbitrary SU($N$) irreps. It is well-suited for numerical implementation; we provide a well-tested computer code for download and online use. Possible applications of our code include numerical treatments of quantum many-body systems using the numerical renormalization group (NRG), the density matrix renormalization group (DMRG), and general tensor network methods.