During the presentation I will introduce the formalism of tensor networks and introduce their relevance to describe the basic states of many-body systems. Then I will introduce the simplest model with topological order presented by Alexei Kitaev, known as the toric code. On his example, I will construct a Projected Entangled Pair States (PEPS) tensor network that describes the basic state of the model and will present the purpose of my project, ie, investigating anion excitation statistics.