Competition between charge-density-wave and superconducting orders on eight-leg square Hubbard cylinders

The issue of whether $d$-wave superconductivity (SC) occurs in the square-lattice Hubbard model with $U$ of order of the bandwidth has been one of the most debated issues to emerge from the study of high temperature SC. Here, we report variational results on eight-leg cylinders with next-nearest-nei