Bounds on correlation functions of quantum rotators

We derive a McBryan-Spencer bound to the correlation function of a one-dimensional array of quantum rotators in the Villain approximation of the cosine interaction. We obtain the partition function of the system in the gas representation and establish a lower bound on the external charges correlation function. We also discuss the possible existence of a Kosterlitz-Thouless phase for the quantum rotators in the Villain approximation.