Implications of direct-product ground states in the one-dimensional quantum XYZ and XY spin chains

We state the conditions under which the general spin-s quantum XYZ ferromagnet (H-) and antiferromagnet (H+) with an external magnetic field along one axis, specified by the Hamiltonian H= Jl=1N (JxSlxSl+1x+JySlyS l+1y+JzSlzSl+1z)-h Jl=1NSlz exhibits a fully ordered ground state described by a wave function which is a direct product of single-site wave functions. We present a detailed analysis of the implications for the zero-temperature dynamical properties of this model. In particular, we derive a rigorous relation between the three dynamic structure factors S(q,), =x,y,z at T=0. For the special case of the s=(1/2) anisotropic XY model (Jz=0), these relations are used to determine the dynamic structure factors Sxx(q,) and Syy(q,) at T=0 and h=(JxJy)1/2 in terms of the known dynamic structure factor Szz(q,).