Unconventional Néel and dimer orders in a spin- 1/2 frustrated ferromagnetic chain with easy-plane anisotropy

We study the ground-state phase diagram of a one-dimensional spin- 1/2 easy-plane XXZ model with a ferromagnetic nearest-neighbor (NN) coupling J ₁ and a competing next-nearest-neighbor (NNN) antiferromagnetic coupling J₂ in the parameter range 0< J₂/ | J ₁| <0.4. When J₂ / | J₁ | <1/4, the model is in a Tomonaga-Luttinger liquid phase which is adiabatically connected to the critical phase of the XXZ model of J₂=0. On the basis of the effective (sine-Gordon) theory and numerical analyses of low-lying energy levels of finite-size systems, we show that the NNN coupling induces phase transitions from the Tomonaga-Luttinger liquid to gapped phases with either Néel or dimer order. Interestingly, these two types of ordered phases appear alternately as the easy-plane anisotropy is changed toward the isotropic limit. The appearance of the antiferromagnetic (Néel) order in this model is remarkable, as it is strongly unfavored by both the easy-plane ferromagnetic NN coupling and the antiferromagnetic NNN coupling in the classical-spin picture. We argue that emergent trimer degrees of freedom play a crucial role in the formation of the Néel order.