Order by projection in the single-band Hubbard model: A density matrix renormalization group study

In a Fermi system near or at half-filling, a specific superconducting pairing channel, if not explicitly included in the Hamiltonian, can be boosted by suppressing a competing pairing channel; this is exemplified by the enhancement of extended $s$-wave correlations upon suppressing $s$-wave Cooper pairing. This phenomenon, originally found by the use of generalized uncertainty relations is referred to as order by projection. The case of zero on-site Coulomb interaction in the thermodynamic limit, confirms this mechanism through the analytical solution. In this study, we go further and systematically investigate this mechanism for a strongly correlated fermionic Hubbard model, now with finite on-site interaction, on a square lattice with an extended set of hopping parameters. We explore the behaviors of different pairing channels when one of them is suppressed, utilizing density matrix renormalization group calculations. Our findings provide numerical evidence supporting the existence of order by projection in the strongly correlated system we studied. We also investigate the effect of the strength of Hubbard $U$, next-nearest-neighbor ${t}^{\ensuremath{'}}$, hole doping, as well as finite-size scaling approaching the thermodynamic limit.