  We introduce effective form factors for one-dimensional lattice fermions with
arbitrary phase shifts. We study tau functions defined as series of these form
factors. On the one hand we perform the exact summation and present tau
functions as Fredholm determinants in the thermodynamic limit. On the other
hand simple expressions of form factors allow us to present the corresponding
series as integrals of elementary functions. Using this approach we re-derive
the asymptotics of static correlation functions of the XY quantum chain at
finite temperature.
