  The ground-state phase diagram of a spin-1/2 XXZ chain with competing
ferromagnetic nearest-neighbor (J_1<0) and antiferromagnetic second-neighbor
(J_2>0) exchange couplings is studied by means of the infinite time evolving
block decimation algorithm and effective field theories. For the
SU(2)-symmetric (Heisenberg) case, we show that the nonmagnetic phase in the
range -4<J_1/J_2<0 has a small but finite ferromagnetic dimer order. We argue
that this spontaneous dimer order is associated with effective spin-1 degrees
of freedom on dimerized bonds, which collectively form a valence bond solid
state as in the spin-1 antiferromagnetic Heisenberg chain (the Haldane spin
chain). We thus call this phase the Haldane dimer phase. With easy-plane
anisotropy, the model exhibits a variety of phases including the vector chiral
phase with gapless excitations and the even-parity dimer and Neel phases with
gapped excitations, in addition to the Haldane dimer phase. Furthermore, we
show the existence of gapped phases with coexisting orders in narrow regions
that intervene between the gapless chiral phase and any one of Haldane dimer,
even-parity dimer, and Neel phases. Possible implications for
quasi-one-dimensional edge-sharing cuprates are discussed.
