Nonperturbative Approach to Luttinger's Theorem in One Dimension

The Lieb-Schultz-Mattis theorem for spin chains is generalized to a wide range of models of interacting electrons and localized spins on a one dimensional lattice. The existence of a low-energy state is generally proved except for special commensurate fillings where a gap may occur. Moreover, the crystal momentum of the constructed low-energy state is 2kF, where kF is the Fermi momentum of the noninteracting model, corresponding to Luttinger's theorem. For the Kondo lattice model, our result implies that kF must be calculated by regarding the localized spins as additional electrons.