Doing time evolution of quantum systems with large local bond dimension is hard. After proposing ppDMRG [1] it became a little bit easier, but if one is only interested in spectral functions a possibly less demanding approach is to use the Chebyshev expansion [2]. This project aims at understanding the limitations with respect to an energy truncation. Furthermore, the investigation of the spin-1 bilinear-biquadratic Heisenberg model is not finished since for the determination of the order of the critical-to-ferromagnetic phase transition high-precision results in the area close to this transition are needed. Our up-to-date results in this area lack precision due to rapid growth of the correlation length in the system. Appropriate calculations require large amount of RAM, which makes access to `fat' nodes on Rackham essential. [1] https://scipost.org/submissions/scipost_202009_00002v2/ (accepted) [2] https://journals.aps.org/prb/abstract/10.1103/PhysRevB.83.195115