  The static structure factor S(q) of frustrated spin-1/2 chains with isotropic
exchange and a singlet ground state (GS) diverges at wave vector q_m when the
GS has quasi-long-range order (QLRO) with periodicity 2\pi/q_m but S(q_m) is
finite in bond-order-wave (BOW) phases with finite-range spin correlations.
Exact diagonalization and density matrix renormalization group (DMRG)
calculations of S(q) indicate a decoupled phase with QLRO and q_m = \pi/2 in
chains with large antiferromagnetic exchange between second neighbors. S(q_m)
identifies quantum phase transitions based on GS spin correlations.
