Chiral Anomaly and Spin Gap in One-Dimensional Interacting Fermions

TL;DR

This paper develops a semiclassical approach to analyze one-dimensional interacting fermion systems, revealing the emergence of a spin gap in double-chain systems and connecting chiral anomaly with spin-charge separation.

Contribution

It introduces a new semiclassical method based on Berry phase and chiral anomaly to identify strong-coupling fixed points in 1D fermion systems.

Findings

Massless Tomonaga-Luttinger liquid in single chains

Spin gap opens in double-chain systems

Connection between chiral anomaly and spin gap states

Abstract

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