Competing phases in spin-1/2 J₁-J₂ chain with easy-plane anisotropy

We summarize our theoretical findings on the ground-state phase diagram of the spin-1/2 XXZ chain having competing nearest-neighbor (J₁) and antiferromagnetic next-nearest-neighbor (J₂) couplings. Our study is mainly concerned with the case of ferromagnetic J₁, and the case of antiferromagnetic J₁ is briefly reviewed for comparison. The phase diagram contains a rich variety of phases in the plane of J₁/J ₂ versus the XXZ anisotropy Δ: vector-chiral phases, Néel phases, several dimer phases, and Tomonaga-Luttinger liquid phases. We discuss the vector-chiral order that appears for a remarkably wide parameter space, successive Néel-dimer phase transitions, and an emergent nonlocal string order in a narrow region of ferromagnetic J₁ side.