CHIRAL ANOMALY AND SPIN GAP IN ONE-DIMENSIONAL INTERACTING FERMIONS

Semiclassical approach has been developed for the one-dimensional inte racting fermion systems. Starting from the incommensurate spin density wave (SDW) mean field state for the repulsive Hubbard model in 1D, th e non-Abelian bosonized Lagrangian describing the spin-charge separati on is obtained. The Berry phase term is derived from the chiral anomal y, and we obtain the massless Tomonaga-Luttinger liquid in the single chain case while the spin gap opens in the double-chain system. This a pproach offers a new method to identify the strong-coupling fixed poin t, and its relation to the Abelian bosonization formalism is discussed on the spin gap state. The generalization to higher dimensions is als o discussed.