  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 $J_2$ in
the parameter range $0<J_2/|J_1|<0.4$. When $J_2/|J_1|\lesssim1/4$, the model
is in a Tomonaga-Luttinger liquid phase which is adiabatically connected to the
critical phase of the XXZ model of $J_2=0$. 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 Neel or dimer
order. Interestingly, these two types of ordered phases appear alternately as
the easy-plane anisotropy is changed towards the isotropic limit. The
appearance of the antiferromagnetic (Neel) order in this model is remarkable,
as it is strongly unfavored by both the easy-plane ferromagnetic NN coupling
and 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
Neel order.
