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

TL;DR

This paper investigates the low-energy behavior of two-leg spin-1 antiferromagnetic ladders under external fields, revealing critical phenomena, universality classes, and proposing new theoretical expressions for string order parameters.

Contribution

It extends the analysis of spin-1 ladders to include external fields and modifications, providing new critical curve predictions and field-theoretical expressions for order parameters.

Findings

Critical curves depend on field type and coupling strength.

Uniform field induces a universal critical state with central charge c=1.

Staggered field does not produce singular phenomena.

Abstract

This study addresses low-energy properties of 2-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 $J_\perp$ region, degenerate perturbation theory applied to spin-$S$ ladders predicts $2S$ critical curves in the parameter space $(J_\perp, H)$ 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 $J_\perp$. 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 is also proposed.