How to control pairing fluctuations: SU(2) slave-rotor gauge theory of the Hubbard model

We study how to incorporate Mott physics in the BCS-type superconductor, motivated from the fact that high $T_c$ superconductivity results from a Mott insulator via hole doping. The U(1) slave-rotor representation was proposed to take local density fluctuations into account non-perturbatively, describing the Mott-Hubbard transition at half filling. Since this decomposition cannot control local pairing fluctuations, the U(1) slave-rotor representation does not give a satisfactory treatment for charge fluctuations. Extending the U(1) slave-rotor representation, we introduce an SU(2) slave-rotor representation to allow not only local density fluctuations but also local pairing excitations. We find an SU(2) slave-rotor gauge theory of the Hubbard model in terms of two kinds of collective boson excitations associated with density and pairing fluctuations that interact with gapless fermion excitations via SU(2) gauge fluctuations. An interesting observation in this effective description is that phase fluctuations of fermion pairs arise as SU(2) gauge fluctuations. Thus, fermion-pairing excitations can be controlled by dynamics of collective bosons in the SU(2) slave-rotor gauge theory. Performing the standard saddle-point analysis based on the SU(2) slave-rotor action, we find ......