Two particle correlations and orthogonality catastrophe in interacting Fermi systems

TL;DR

This paper investigates two-particle correlations in interacting Fermi systems, revealing how these correlations depend on dimensionality and how the orthogonality catastrophe manifests in finite two-dimensional Fermi liquids.

Contribution

It provides a detailed analysis of two-particle correlations and the orthogonality catastrophe in finite interacting Fermi systems, extending understanding in two and higher dimensions.

Findings

Particles on the same Fermi point can be correlated in low dimensions.

Particles on different Fermi points are uncorrelated in dimensions greater than one.

The orthogonality effect in a two-dimensional Fermi liquid is finite.

Abstract

The wave function 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 unabiguous picture of the two-particle correlations. As recently pointed out by Anderson, in two or lower 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 dimensions 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.