Effective pairing interaction in the two-dimensional Hubbard model within a spin rotationally invariant approach

TL;DR

This paper develops a rotationally-invariant approach to the 2D Hubbard model, revealing how gauge fields act as a pairing 'glue' for fermions and identifying the conditions for attractive pairing.

Contribution

It introduces a gauge field formulation of the Hubbard model that elucidates the pairing mechanism in the low-energy limit.

Findings

Gauge fields act as the pairing 'glue' for fermions.

Attractive pairing potential exists only in a narrow U/t range.

The approach provides a new analytical framework for strongly correlated systems.

Abstract

We implement the rotationally-invariant formulation of the two-dimensional Hubbard model, with nearest-neighbors hopping $t$, which allows for the analytical study of the system in the low-energy limit. Both U(1) and SU(2) gauge transformations are used to factorize the charge and spin contributions to the original electron operator in terms of the corresponding gauge fields. The Hubbard Coulomb energy $U$ term is then expressed in terms of quantum phase variables conjugate to the local charge and variable spin-quantization axis, providing a useful representation of strongly correlated systems. It is shown that these gauge fields play a similar role as phonons in the BCS theory: they act as the "glue" for fermion pairing. By tracing out gauge degrees of freedom, the form of paired states is established and the strength of the pairing potential is determined. It is found that the attractive pairing potential in the effective low-energy fermionic action is non-zero in a rather narrow range of $U/t$.