Numerical investigations of the Schwinger model and selected quantum spin models

Numerical investigations of the XY model, the Heisenberg model and the J-J' Heisenberg model are conducted, using the exact diagonalisation, the numerical renormalisation and the density matrix renormalisation group approach. The low-lying energy levels are obtained and finite size scaling is performed to estimate the bulk limit value. The results are found to be consistent with the exact values. The DMRG results are found to be most promising.The Schwinger model is also studied using the exact diagonalisation and the strong coupling expansion. The massless, the massive model and the model with a background electric field are explored. Ground state energy, scalar and vector particle masses and order parameters are examined. The achieved values are observed to be consistent with previous results and theoretical predictions. Path to the future studies is outlined.