Electrical and mechanical properties of strongly-correlated systems

Full text: The electrical and mechanical properties of ultrasmall structures are a subject of considerable current interest. The behaviour of such structures is fundamentally different from that of conventional electronic and mechanical systems due to a variety of novel quantum mechanical effects. Furthermore, the effects of electron-electron interactions are typically enhanced in systems of reduced dimensionality, leading to nonperturbative effects, such as the breakdown of Fermi liquid behaviour in one-dimensional (1D) metals. We study two different variants of the Heisenberg quantum spin chain. The first variant is a usual Heisenberg quantum spin chain where locally the exchange couplings are modified, for instance in the simplest case only one exchange coupling is different from the others. This situation can be regarded as a model for a weak junction in a quantum wire. The second variant is a model recently introduced. In its simplest form it is a Heisenberg quantum spin chain where the exchange couplings to the right and left of one particular site are modified and there is a three--spin coupling in addition creating an impurity in the chain. This central site may be considered as representing a quantum dot coupled to the chain. The analytical calculations are supported by extensive numerical calculations using mainly density-matrix renormalization group (DMRG) algorithms