Low-dimensional correlated particle systems: Exact results for groundstate and thermodynamic quantities

A one-dimensional fermion model with bond charge-interactions as well as Hubbard-type interactions is investigated exactly. The large distance asymptotics of the density-density and pair correlations are calculated. The system shows Luther-Emery liquid behaviour with a crossover from a density-density dominated regime to one with dominant pair correlations. Furthermore, the integrable tJ chain is studied at finite temperatures. Some concepts for this analysis are introduced, notably the Trotter-Suzuki mapping and the quantum transfer matrix. Finally, the specific heat is presented and its structure discussed.