Nonperturbative Approach to Luttinger's Theorem in One Dimension

Abstract

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 ${2k}_{F}$, where ${k}_{F}$ is the Fermi momentum of the noninteracting model, corresponding to Luttinger's theorem. For the Kondo lattice model, our result implies that ${k}_{F}$ must be calculated by regarding the localized spins as additional electrons.