An introduction to numerical methods in low-dimensional quantum systems

this is an introductory course to the lanczos method and density matrix renormalization group algorithms (dmrg), two among the leading numerical techniques applied in studies of low-dimensional quantum models. the idea of studying the models on clusters of a finite size in order to extract their physical properties is briefly discussed. the important role played by the model symmetries is also examined. special emphasis is given to the dmrg.