 The algorithm, based on the Matrix Product States formalism, is highly efficient when the amount of entanglement in the system is limited, a requirement fulfilled by a large class of quantum many-body systems in one dimension.There is nowadays a considerable interest in the field of quantum theory for computational methods well-suited to the physics of many-body systems.Considering the inherent difficulties of simulating general quantum many-body systems, the exponential increase in parameters with the size of the system, and correspondingly, the high computational costs, one solution would be to look for numerical methods that deal with special cases, where one can profit from the physics of the system.