Theory of the symmetric Wolff model. I. Weak-coupling-long-time-zero-temperature limit

Abstract

The local single-particle and density correlation functions for the symmetric Wolff model are derived analytically. The scattering channels are separated by means of the Stratonovich-Hubbard transformation and the associated one-body problem is solved explicitly in the long-time limit. A stationary phase argument yields expressions for the correlation functions in the weak-coupling limit. The single-particle correlation function acquires a time-dependent phase shift due to the readjustment of the spin-up and spin-down Fermi systems. The spin-up and spin-down Fermi systems relax on a timescale determined by the inverse bandwidth. In the intermediate- and strong-coupling regimes many-body effects intervene and the calculation breaks down.