This is the repo for my bachelor thesis. Here is the abstract:
The approach to the many body problem is in general strongly impaired by the exponential scaling in the number of components of the computational costs. However, for a large class of low-dimensionality models constraints on the entanglement structure of ground states allow an efficient study, with renormalization algorithms based on ansatzes which optimally capture such structure. Both can be naturally formulated in a diagrammatic language, that of Tensor Networks. In this treatise we will give a general introduction and then we will consider specifically the one-dimensional case, introducing Matrix Product States and the Density Matrix Renormalization Group and illustrating a simple application.