Low-energy properties of two-leg spin-1 antiferromagnetic ladders with commensurate external fields and their extensions

Abstract

This study addresses low-energy properties of two-leg spin-1 ladders with antiferromagnetic (AF) intrachain coupling under a uniform or staggered external field $H$, and a few of their modifications. The generalization to spin-$S$ ladders is also discussed. In the strong AF rung(interchain)-coupling ${J}_{\ensuremath{\perp}}$ region, degenerate perturbation theory applied to spin-$S$ ladders predicts $2S$ critical curves in the parameter space $({J}_{\ensuremath{\perp}},H)$ for the staggered-field case, in contrast to $2S$ finite critical regions for the uniform-field case. All critical areas belong to a universality with central charge $c=1$. On the other hand, we employ Abelian and non-Abelian bosonization techniques in the weak rung-coupling region. They show that in the spin-1 ladder, a sufficiently strong uniform field engenders a $c=1$ critical state regardless of the sign of ${J}_{\ensuremath{\perp}}$, whereas the staggered field is expected not to yield any singular phenomena. From the bosonization techniques, new field-theoretical expressions of string order parameters in the spin-1 systems are also proposed.