  The Hubbard model is an important tool to understand the electrical
properties of various materials. More specifically, on the honeycomb lattice it
is used to describe graphene predicting a quantum phase transition from a
semimetal to a Mott insulating state. In this work two different numerical
techniques are presented that have been employed for simulations of the Hubbard
model: The Hybrid Monte Carlo algorithm on the one hand allowed us to simulate
unprecedentedly large lattices, whereas Tensor Networks can be used to
completely avoid the sign problem. Respective strengths and weaknesses of the
methods are discussed.
