Motivated by the recent discovery of the anomalously nearest-neighbor attraction arising from the electron-phonon coupling, we quantitatively investigate the enhancing effects of this additional attractive channel on the
d-wave superconductivity based on dynamic cluster quantum Monte Carlo calculations of a doped two-dimensional extended Hubbard model with nearest-neighbor attraction $\ensuremath{-}V$. Focusing on the range of $0<\ensuremath{-}V/t\ensuremath{\le}2$, our simulations indicate that the dynamics of
d-wave projected pairing interaction is attractive at all frequencies and increases with
∣V∣. Moreover, turning on $\ensuremath{-}V$ attraction enhances the $(\ensuremath{\pi},\ensuremath{\pi})$ spin fluctuations but only enhances (suppresses) the charge fluctuations for small (large) momentum transfer. Thus, at $V/t=\ensuremath{-}1$ relevant to the ``holon folding branch'', the charge fluctuations are insufficient to compete with the
d-wave pairing interaction strengthened by enhanced spin fluctuations. Our work suggests the underlying rich interplay between the spin and charge fluctuations in giving rise to the superconducting properties.
Understanding competing instabilities in systems with correlated fermions remains one of the holy grails of modern condensed matter physics. Among the fermionic lattice models used to this effect, the extended Hubbard model occupies a prime place due to the potential relevance of its repulsive and attractive versions for both electronic materials and artificial systems. Using the recently introduced multichannel fluctuating field approach, we address the interplay of fluctuations in the charge density wave,
s-wave superconducting, and phase separation channels in the attractive extended Hubbard model. Despite the fact that this model has been intensively studied for decades, our approach allows us to identify a phase that has not been analyzed before and which is characterized by the coexistence of collective
s-wave superconducting and phase separation fluctuations. Our findings resonate with previous observations of interplaying phase separation and superconducting phases in electronic systems, most importantly in high-temperature superconductors.
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.