Scattering and Pairing by Exchange Interactions

TL;DR

This paper investigates a quantum many-body system with exchange interactions involving two fermions and one boson, revealing localized bound pairs and detailed scattering properties relevant to cuprate superconductors.

Contribution

It introduces a mathematical analysis of off-diagonal exchange interactions in a fermion-boson system, including the effects of Hubbard repulsion, and characterizes bound states and scattering behaviors.

Findings

Existence of exponentially localized bound fermion pairs.

Detailed dispersion relation for bound pairs.

Scattering properties in unbound and bound channels.

Abstract

Quantum interactions exchanging different types of particles play a pivotal r\^{o}le in quantum many-body theory, but they are not sufficiently investigated from a mathematical perspective. Here, we consider a system made of two fermions and one boson, in order to study the effect of such an off-diagonal interaction term, having in mind the physics of cuprate superconductors. Additionally, our model also includes a generalized Hubbard interaction (i.e., a general local repulsion term for the fermions). Regarding pairing, exponentially localized dressed bound fermion pairs are shown to exist and their effective dispersion relation is studied in detail. Scattering properties of the system are derived for two channels: the unbound and bound pair channels. We give particular attention to the regime of very large on-site (Hubbard) repulsions, because this situation is relevant for cuprate superconductors.