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Within the 1D Hubbard model linear closed chains with various numbers ofsites are considered in Self Consistent Random Phase Approximation (SCRPA).Excellent results with a minimal numerical effort are obtained for 2+4n sitescases, confirming earlier results with this theory for other models. However,the 4n sites cases need further considerations. SCRPA solves the two sitesproblem exactly. It therefore contains the two electrons and high density Fermigas limits correctly.Comment: 17 pages, 17 figure

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