A Mechanism for Ferrimagnetism and Incommensurability in One-Dimensional Systems

A mechanism for ferrimagnetism in (1+1)-dimensions is discussed. The ferrimagnetism is cased by interactions described by operators with non-zero conformal spin. Such interactions appear in such problems as the problem of tunneling between Luttinger liquids and the problem of frustrated spin ladder. I present exact solutions for a representative class of models containing such interactions together with a simple mean field analysis. It is shown that the interactions (i) dynamically generate static oscillations with a wave vector dependent on the coupling constant, (ii) give rise to a finite magnetic moment at $T = 0$ accompanied by the soft mode with a non-relativistic ({\it ferromagnetic}) dispersion $E \sim k^2$, (iii) generate massive (roton) modes.