Effective one-dimensional models including two-particle interaction from matrix product states

In this thesis a method for deriving effective models for one-dimensional spin systems is introduced. It is based on matrix product state (MPS) and exploits translation invariance to efficiently work in the thermodynamic limit. It is tested on two analytically solvable models: The ferromagnetic spin-\textonehalf\ Heisenberg chain in an external field, and the transverse magnetic field Ising model (TFIM). The previously developed ansatz for one-particle states is extended to the description of two-particle states. The challenges of this extension and different choices for a basis of the two-particle space are discussed. Results for the two-particle spectral weight in the TFIM and for quasi-particle scattering in both models are provided