Chiral order of spin-1/2 frustrated quantum spin chains

The ordering of the frustrated S=1/2 XY spin chain with the competing nearest- and next-nearest-neighbor anti-ferromagnetic couplings, J1 and J2, is studied by using the density-matrix renormalization-group method. It is found that besides the wellknown spin-fluid and dimer phases the chain exhibits a gapless "chiral" phase characterized by the spontaneous breaking of parity, in which the long-range order parameter is a chirality, (kappa)l=SxlSyl+1 – Syl Sxl+1, whereas the spin correlation decays algebraically. The dimer phase is realized for 0.33 ~~1.26.