SU(2) slave-rotor theory of the attractive Hubbard model

TL;DR

This paper introduces an SU(2) slave-rotor framework for the attractive Hubbard model, enabling a unified treatment of superconductivity and charge density wave fluctuations, and reveals a second order phase transition.

Contribution

It extends the slave-rotor approach to the attractive Hubbard model using SU(2) variables, incorporating order parameter fluctuations beyond mean field.

Findings

Demonstrates a second order phase transition driven by slave-rotor softening.

Provides an effective SU(2) slave-rotor action for the attractive Hubbard model.

Shows the importance of order parameter fluctuations in phase transition analysis.

Abstract

Extending the U(1) slave-rotor representation\cite{FG_SRR} of the repulsive Hubbard model, we propose an SU(2) slave-rotor decomposition for the attractive Hubbard model, where the SU(2) slave-rotor variables represent order parameter fluctuations associated with superconductivity and charge density wave. This decomposition method allows us to modify the standard Hartree-Fock mean field theory by incorporating order parameter fluctuations on an equal footing. Deriving an effective SU(2) slave-rotor action from the attractive Hubbard model, and analyzing it at the mean field level, we demonstrate a second order phase transition driven by softening of the slave-rotor variables.