Non-perturbative approach to Luttinger's theorem in one dimension

Details Non-perturbative approach to Luttinger's theorem in one dimension Non-perturbative approach to Luttinger's theorem in one dimension

1997-01-21

arxiv.org/abs/cond-mat/9701141v2

Phys. Rev. Lett. 79, 1110 (1997)

Physics

Condensed Matter

Strongly Correlated Electrons

Note added on the rigorous proof given by H. Tasaki; also added some references; 5 pages, REVTEX (no figure)

Scientific paper

10.1103/PhysRevLett.79.1110

The Lieb-Schultz-Mattis theorem for spin chains is generalized to a wide range of models of interacting electrons and localized spins in 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 non-interacting 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.

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