Quantum chiral phases in frustrated easy-plane spin chains

The phase diagram of antiferromagnetic spin-$S$ chain with $\mathrm{XY}$-type anisotropy and frustrating next-nearest-neighbor interaction is studied in the limit of large integer S with the help of a field-theoretical approach. It is shown that the existence of gapless and gapped chiral phases found in recent numerical studies [M. Kaburagi et al., J. Phys. Soc. Jpn. 68, 3185 (1999); T. Hikihara et al., J. Phys. Soc. Jpn. 69, 259 (2000)] is not specific for $S=1,$ but is rather a generic large-$S$ feature. Estimates for the corresponding transition boundaries are obtained, and a sketch of the typical phase diagram is presented. It is also shown that frustration stabilizes the Haldane phase against the variation of the anisotropy.