  Within the 1D Hubbard model linear closed chains with various numbers of
sites are considered in Self Consistent Random Phase Approximation (SCRPA).
Excellent results with a minimal numerical effort are obtained for 2+4n sites
cases, confirming earlier results with this theory for other models. However,
the 4n sites cases need further considerations. SCRPA solves the two sites
problem exactly. It therefore contains the two electrons and high density Fermi
gas limits correctly.
