Correlation Functions in the XXO Heisenberg Chain and their Relations with Spectral Shapes

The spectral shape of one dimensional systems (describing for instance the behaviour of Frenkel excitons) is approached through the exactly solvable model of XXO Heisenberg quantum spin chain in a transverse magnetic field. Some results for finite size chains concerning 2N-point correlators are presented in details. In particular the finite lattice, finite temperature 2-point correlators are explicitely worked out. Moreover, results in closed form are given for 2N-point correlators in the most general situation (finite lattice and thermodynamic limit, finite temperature, finite space and/or time separations). Their relations with frequency moments of the spectral shape are pointed out and the connection with moment expansion through continued fraction representation is given. PACS: 75.10.Jm , 05.30.-d