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, 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 a gapless "chiral" phase characterized by the spontaneous breaking of parity, in which the long-range order parameter is a chirality, kappa (l) =(SlSl+1y)-S-x - S-l(y) S-l+1(x), whereas the spin correlation decays algebraically. The dimer phase is realized for 0.33 less than or similar to j = J(2)/J(1) less than or similar to 1.26 while the chiral phase is realized for j greater than or similar to 1.26.