Ground-state phase diagram of a spin-1/2 frustrated XXZ ladder

TL;DR

This paper maps the ground-state phase diagram of a frustrated spin-1/2 XXZ ladder, revealing multiple gapped and critical phases, and elucidates the effects of exchange anisotropy and frustration on phase transitions.

Contribution

It extends previous isotropic models to the XXZ case, uncovering a richer phase diagram with new phases and complex interplay between dimer attraction and anisotropy.

Findings

Identified four gapped featureless phases, including rung singlet and Haldane phases.

Discovered the crossing of transition lines replacing the Haldane-CD transition in the XXZ model.

Revealed complex competition among phases in the easy-plane regime.

Abstract

We study the ground-state phase diagram of a spin-$\frac{1}{2}$ frustrated XXZ ladder, in which two antiferromagnetic chains are coupled by competing rung and diagonal interactions, $J_\perp$ and $J_\times$. Previous studies on the isotropic model have revealed that a fluctuation-induced effective dimer attraction between the legs stabilizes the columnar dimer (CD) phase in the highly frustrated regime $J_\perp\approx 2J_\times$, especially for ferromagnetic $J_{\perp, \times}<0$. By means of effective field theory and numerical analyses, we extend this analysis to the XXZ model, and obtain a rich phase diagram. The diagram includes four gapped featureless phases with no symmetry breaking: the rung singlet (RS) and Haldane phases as well as their twisted variants, the RS* and Haldane* phases, which are all distinct in the presence of certain symmetries. Significantly, the Haldane-CD transition point in the isotropic model turns out to be a crossing point of two transition lines in the XXZ model, and the stripe N\'eel and RS* phases appear between these lines. This indicates a nontrivial interplay between the effective dimer attraction and the exchange anisotropy. In the easy-plane regime, the four featureless phases and two critical phases are found to compete in a complex manner depending on the signs of $J_{\perp, \times}$.