Title:

Theory of properties of some onedimensional systems

This thesis consists in a theoretical study of some onedimensional models. Special attention is given to simple but nontrivial soluble models. The study starts with a resume of the Green function method which is the formalism used throughout the work. A discussion of coupled electronphonon and spinphonon systems is presented and a decoupling scheme introduced. The approximation gives the transition temperature for onedimensional systems exactly, namely T = 0, and consequently represents a great improvement on the meanfield approximation. The impure XYchain in a transverse field is studied and the formal solution presented. The static and timedependent correlations are discussed, and the effect of the boundary term reviewed in details. The oneimpurity case is solved for the isotropic chain, and it is shown how to derive from it the open chain result in the thermodynamic limit. The heatflux operator is obtained for the impure isotropic chain by solving the continuity equation for energy density. The dynamics of the onedimensional transverse Ising model is discussed within several approximations. The limitations of each approximation are examined in detail and the timedependent correlations are calculated using the most successful approximation. It is also shown that this approximation is only valid in the high temperature limit in which case no critical behaviour is to be observed. The oneimpurity solution of the isotropic impure XYchain is extended to many impurities in two different cases. In the first case the specific heat of the dilute chain is calculated in the framework of the average tmatrix approximation, and the results compared with exact numerical calculations for finite chains. In the second case the specific heat and thermal conductivity of the isotropic XYchain in a random transverse field are calculated using the coherentpotential approximation (CPA). The results are used to explain the low temperature thermal properties of praseodymium ethyl sulphate. Finally, two interacting systems, an electronphonon system and a spinphonon system, are studied after a brief discussion of the socalled Peierls instability. The first model is solved exactly in the framework of the approximation discussed at the beginning of the work. It presents a giant Kohn anomaly at zero temperature which drives a Peierls transition. The renormalized modes are discussed, and the real and imaginary parts of the phonon propagator are presented for wave vector ^{andpi;}andfrasl;_{a} and several coupling constants and temperatures. The spinphonon system is also studied in the framework of the approximation discussed initially in the work, and it is chosen in such a way that the relevant properties are given in terms of Green functions calculated in the transverse Ising model. The results obtained for the dynamics of this model are used, and since they are valid only in the high temperature limit, the discussion is restricted to this temperature region. Since this region is far away from the critical one, no critical behaviour is observed, and the study is restricted to a simple discussion of modes. The real and imaginary parts of the renormalized phonon propagator are presented for the wave vector ^{andpi;}andfrasl;_{a}, high temperature and various coupling constants.
