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This state is a zero temperature quantum liquid that does not break translational symmetry, and yet, the Fermi surface encloses a volume smaller than the large one given by the Luttinger theorem. The particle number enclosed by the small Fermi surface in the LvvFL equals the doping level $p$, not the total electron number $n_e=1-p$. 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This state is a zero temperature quantum liquid that does not break translational symmetry, and yet, the Fermi surface encloses a volume smaller than the large one given by the Luttinger theorem. The particle number enclosed by the small Fermi surface in the LvvFL equals the doping level $p$, not the total electron number $n_e=1-p$. 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