Theoretical studies of quantum spin systems

In this thesis we present the results of calculations of the properties of quantum spin systems. The majority of the work is concerned with one dimensional spin chains and the particular effects that reduced dimensionality produce. The final chapter describes some earlier work on mixed valence manganite compounds. We demonstrate one derivation of the Heisenberg Hamiltonian and discuss its applicability to modelling magnetic systems both in three and one dimension. We discuss systems that are exactly soluble and the failure of spin wave theory in I-D. The Density-Matrix Renormalisation Group (DMRG) method is discussed in detail as is the extension to finite temperature (TMRG). We show results of calculations on a number of S=1/2 and S=l models and fundamental differences in their excitation spectra is observed. The thermodynamics of these systems have been obtained over a wide temperature range. In addition, excellent agreement with experiment is shown for a number of quasi one dimensional compounds. The DMRG and TMRG are shown to be very competitive and accurate methods of studying such systems, especially in the case of gapped systems. The final chapter discusses the role of correlated magnetic clusters in determining the magnetic properties of mixed valence manganites at temperatures near the Curie temperature. Our results are supported by recent direct experimental observation of the formation of these clusters. We also briefly discuss some preliminary results regarding the effect of an interface on the electronic and magnetic properties of these compounds.