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 antiferromagnetic couplings, J_1 and J_2, is studied by using the density-matrix renormalization-group method. It is found that besides the well-known spin-fluid and dimer phases the chain exhibits gapless `chiral' phase characterized by the spontaneous breaking of parity, in which the long-range order parameter is a chirality, \kappa _l=S_l^xS_{l+1}^y-S_l^yS_{l+1}^x, whereas the spin correlation decays algebraically. The dimer phase is realized for 0.33 \lsim j = J_2/J_1 \lsim 1.26 while the chiral phase is realized for j \gsim 1.26.