COMPETING PHASES IN SPIN-½ J₁-J₂ CHAIN WITH EASY-PLANE ANISOTROPY

Abstract

We summarize our theoretical findings on the ground-state phase diagram of the spin-½ XXZ chain having competing nearest-neighbor (J 1 ) and antiferromagnetic next-nearest-neighbor (J 2 ) couplings. Our study is mainly concerned with the case of ferromagnetic J 1 , and the case of antiferromagnetic J 1 is briefly reviewed for comparison. The phase diagram contains a rich variety of phases in the plane of J 1 /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 J 1 side.