SU(N) evolution of a frustrated spin ladder

Abstract

Recent studies indicate that the weakly coupled, ${J}_{\ensuremath{\perp}}\ensuremath{\ll}J,$ spin-1/2 Heisenberg antiferromagnet with next-nearest-neighbor frustration, ${J}_{\ifmmode\times\else\texttimes\fi{}},$ supports massive spinons for ${J}_{\ifmmode\times\else\texttimes\fi{}}{=J}_{\ensuremath{\perp}}/2.$ The straightforward $\mathrm{SU}(N)$ generalization of the low-energy ladder Hamiltonian yields two independent $\mathrm{SU}(N)$ Thirring models with $N\ensuremath{-}1$ multiplets of massive ``spinon'' excitations. We study the evolution of the complete set of low energy dynamical structure factors using form factors. Those corresponding to the smooth (staggered) magnetizations are qualitatively different (the same) in the $N=2$ and $N>2$ cases. The absence of single-particle peaks preserves the notion of spinons stabilized by frustration. In contrast to the ladder, we note that the $\stackrel{\ensuremath{\rightarrow}}{N}\ensuremath{\infty}$ limit of the four chain model is not a trivial free theory.