Density Matrix Renormalisation Group Variants for Spin Systems

Abstract

This thesis gives an extension for the Density Matrix Renormalisation Group (DMRG) to two dimensions and described a newly developed combination of the DMRG and a Green Function Monte Carlo simulation (GFMC). The first two chapters focus on the DMRG method. The properties are reviewed and it is shown that good quality results can be obtained for two-dimensional systems through finite-size scaling. In the third and fourth chapter the properties of the two-dimensional frustrated Heisenberg model are analysed using a similar combination of DMRG and finite-size scaling. The final chapter presents the combination of the DMRG and GFMC with Stochastic Reconfiguration (Sorella, Capriotti cond-mat/9902211) We find an intermediate phase between Neel and collinear long-range order. This phase shows spatial inhomogeneities with a tendency towards plaquette formation.