Hosted by: Igor Zaliznyak

I will give a brief introduction to tensor network states with focus on exploiting all symmetries, abelian and non-abelian alike. I will briefly motivate a generic framework for finite-dimensional Lie algebras, which has been fully implemented in the tensor library QSpace [1]. The latter was already put under extensive scrutiny over the past couple of years. Along it already also gave rise to a range of excellent applications. Here, in particular, I will briefly highlight 1D density matrix renormalization group (DMRG) calculations on SU(N) Heisenberg ladders, 2D projected entangled pair state (PEPS) simulations on Spin-1 Kagome [2], and infinite-dimensional dynamical mean-field theory (DMFT) simulations on Hund's metals [3]. [1] A. Weichselbaum, Annals of Physics 327, 2972 (2012) [2] Liu et al., PRB 91 (R), 060403(R) (2015) [3] Stadler et al. PRL 115, 136401 (2015)