Self-consistent random phase approximation: Application to the Hubbard model for finite number of sites

Within the one-dimensional Hubbard model linear closed chains with various numbers of sites are considered in the self-consistent random phase approximation (SCRPA). Excellent results with a minimal numerical effort are obtained for $(2+4n)$-site cases, confirming earlier results with this theory for other models. However, the $4n$-site cases need further consideration. The SCRPA solves the two-site problem exactly. It therefore contains the two-electron and high-density Fermi gas limits correctly.