Electron pair forming in an integrable model

TL;DR

This paper analyzes an integrable lattice model where phonons interact with electron pairs, revealing an exact solution that shows a ground state with paired electrons and a kinetic energy gap due to pairing effects.

Contribution

It provides an analytical solution for a lattice model with electron-phonon interactions, illustrating the formation of electron pairs and energy gaps in an integrable system.

Findings

Exact eigenvalues and eigenvectors are derived.

Ground state features a Fermi sea with electron pairs.

A kinetic energy gap emerges due to pairing effects.

Abstract

We consider a lattice model in which phonons scatter with pairs of electrons. All eigenvalues and eigenvectors can be obtained analytically. For a suitable choice of parameters the ground state consists of a Fermi sea of non-interacting electrons, with on top a layer of paired electrons. The binding energy of the electron pairs is partly cancelled by an increased kinetic energy. This results in a gap in the kinetic energy spectrum of the electrons.