Two particle correlations and orthogonality catastrophe in interacting Fermi systems

The wavefunction of two fermions, repulsively interacting in the presence of a Fermi sea, is evaluated in detail. We consider large but finite systems in order to obtain an unambiguous picture of the two-particle correlations. As recently pointed out by Anderson, in d ≤ 2 dimensions the particles may be correlated even when situated on the Fermi surface. The ”partial exclusion principle” for two particles with opposite spin on the same Fermi point is discussed, and related to results from the T-matrix approximation. Particles on different Fermi points are shown to be uncorrelated in d > 1. Using the results for the two-particle correlations we find that the orthogonality effect induced by adding an extra particle to a (tentative) two-dimensional Fermi liquid is finite.