Generic gauge fields in the Hubbard model: emergence of pairing interaction

TL;DR

This paper extends the SU(2) approach to the Hubbard model to include charge degrees of freedom, revealing that emergent gauge fields can mediate pairing interactions similar to phonons in BCS theory.

Contribution

It introduces a framework using U(1) and SU(2) gauge transformations to describe charge and spin separation, showing gauge fields facilitate fermion pairing in the Hubbard model.

Findings

Gauge fields act as pairing 'glue' analogous to phonons.

Paired states are derived by integrating out gauge bosons.

Antiferromagnetic correlations influence pairing mechanisms.

Abstract

The spin-rotationally invariant SU(2) approach to the Hubbard model is extended to accommodate the charge degrees of freedom. Both U(1) and SU(2) gauge transformation are useed to factorize the charge and spin contribution to the original electron operator in terms of the emergent gauge fields. It is shown that these fields play a similar role as phonons in the BCS theory: they provide the "glue" for fermion pairing. By tracing out gauge bosons the form of paired states is established and the role of antiferromagnetic correlations is explicated.