Ground-state phase diagram of a spin-21 frustrated XXZ ladder

We study the ground-state phase diagram of a spin -21 frustrated XXZ ladder, in which two antiferromagnetic chains are coupled by competing rung and diagonal interactions, J1 and JX. 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 J1 ti 2JX, especially for ferromagnetic J1,X < 0. By means of effective field theory and numerical analyses, we extend this analysis to the XXZ model, and we 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 Neel 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 J1,X.