Theory of the symmetric Wolff model. II. Weak-coupling-long-time-low-temperature limit

Abstract

For pt.I see ibid., vol.10, p.2869 (1977). The local single-particle and density correlation functions for the symmetric Wolff model (1961) are studied in the asymptotic weak-coupling-long-time-low-temperature limit. The scattering channels are separated by means of the Stratonovich-Hubbard transformation and the associated one-body problem is solved explicitly in the low-temperature limit. A steepest-descent argument yields expressions for the correlation functions in the weak-coupling limit. The correlation functions are characterised by a time dependent phase shift which decays on a time scale of the order of the bandwidth. In the intermediate and strong coupling regime many-body effects intervene and the calculation breaks down; in that context comments are made on some recent work by Mattis (1976).